People got saved without believing Jesus is God

Neither Jesus, nor Peter nor Paul taught unbelievers that Jesus is God, yet they got saved.

Jesus declared a woman saved who did not believe he was God

One of the Pharisees asked him (Jesus) to eat with him, and he went into the Pharisee’s house and reclined at table. And behold, a woman of the city, who was a sinner, when she learned that he was reclining at table in the Pharisee’s house, brought an alabaster flask of ointment, and standing behind him at his feet, weeping, she began to wet his feet with her tears and wiped them with the hair of her head and kissed his feet and anointed them with the ointment. Now when the Pharisee who had invited him saw this, he said to himself,

“If this man were a prophet, he would have known who and what sort of woman this is who is touching him, for she is a sinner.” And Jesus answering said to him, “Simon, I have something to say to you.” And he answered, “Say it, Teacher.” “A certain moneylender had two debtors. One owed five hundred denarii, and the other fifty. When they could not pay, he cancelled the debt of both. Now which of them will love him more?” Simon answered, “The one, I suppose, for whom he cancelled the larger debt.” And he said to him, “You have judged rightly.” Then turning toward the woman he said to Simon, “Do you see this woman? I entered your house; you gave me no water for my feet, but she has wet my feet with her tears and wiped them with her hair. You gave me no kiss, but from the time I came in she has not ceased to kiss my feet. You did not anoint my head with oil, but she has anointed my feet with ointment. Therefore I tell you, her sins, which are many, are forgiven — for she loved much. But he who is forgiven little, loves little.” And he said to her, “Your sins are forgiven.” Then those who were at table with him began to say among themselves, “Who is this, who even forgives sins?” And he said to the woman, “Your faith has saved you; go in peace.”

-- Luke 7:36-50

Jesus did not tell the woman that he is God. Based on the way the Pharisee addressed Jesus and the way he treated him and thought about him, he definitely did not believe Jesus was God. The Jews back then and even still today do not believe Jesus is God. If the Pharisee did not believe Jesus was God, what are the chances that a sinful woman, who do not study the Torah, understood the Trinity and somehow believed Jesus was God?

Yet, Jesus told her that she is saved because we can assume she confessed her sins with "tears" and Jesus declared "your sins are forgiven" and her "faith has saved" her.

Peter's sermon

But Peter, standing with the eleven, lifted up his voice and addressed them: “Men of Judea and all who dwell in Jerusalem, let this be known to you, and give ear to my words. For these people are not drunk, as you suppose, since it is only the third hour of the day. But this is what was uttered through the prophet Joel:

“‘And in the last days it shall be, God declares, that I will pour out my Spirit on all flesh, and your sons and your daughters shall prophesy, and your young men shall see visions, and your old men shall dream dreams; even on my male servants and female servants in those days I will pour out my Spirit, and they shall prophesy. And I will show wonders in the heavens above and signs on the earth below, blood, and fire, and vapor of smoke; the sun shall be turned to darkness and the moon to blood, before the day of the Lord comes, the great and magnificent day. And it shall come to pass that everyone who calls upon the name of the Lord shall be saved.’ (Joel 2:28-32)

Men of Israel, hear these words: Jesus of Nazareth, a man attested to you by God with mighty works and wonders and signs that God did through him in your midst, as you yourselves know — this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men. God raised him up, loosing the pangs of death, because it was not possible for him to be held by it.

For David says concerning him,

‘I saw the LORD always before me, for He is at my right hand that I may not be shaken; therefore my heart was glad, and my tongue rejoiced; my flesh also will dwell in hope. For You will not abandon my soul to Hades, or let your holy one see corruption. You have made known to me the paths of life; You will make me full of gladness with your presence.’ (Psalm 16:8-11)

Brothers, I may say to you with confidence about the patriarch David that he both died and was buried, and his tomb is with us to this day. Being therefore a prophet, and knowing that God had sworn with an oath to him that he would set one of his descendants on his throne, he foresaw and spoke about the resurrection of the Christ, that he was not abandoned to Hades, nor did his flesh see corruption. This Jesus God raised up, and of that we all are witnesses. Being therefore exalted at the right hand of God, and having received from the Father the promise of the Holy Spirit, he has poured out this that you yourselves are seeing and hearing.

For David did not ascend into the heavens, but he himself says,

‘The LORD said to my Lord, “Sit at my right hand, until I make your enemies your footstool.”’ (Psalm 110:1)

Let all the house of Israel therefore know for certain that God has made him both Lord and Christ, this Jesus whom you crucified.”

Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?” And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to Himself.”

And with many other words he bore witness and continued to exhort them, saying, “Save yourselves from this crooked generation.”

So those who received his word were baptized, and there were added that day about three thousand souls. And they devoted themselves to the apostles' teaching and the fellowship, to the breaking of bread and the prayers. And awe came upon every soul, and many wonders and signs were being done through the apostles. And all who believed were together and had all things in common. And they were selling their possessions and belongings and distributing the proceeds to all, as any had need. And day by day, attending the temple together and breaking bread in their homes, they received their food with glad and generous hearts, praising God and having favor with all the people. And the Lord added to their number day by day those who were being saved.

-- Acts 2:14-47 (ESV)

Peter omits to mention that "anyone need to belief that Jesus is God to receive salvation". If that was a requirement, then those 3000 souls would have been lost.

Peter did explain the difference between God, Jesus and the Holy Spirit, but he never said that they are "equal or the same God".

Paul's sermon in Antioch

Now when Paul and his party set sail from Paphos, they came to Perga in Pamphylia; and John, departing from them, returned to Jerusalem. But when they departed from Perga, they came to Antioch in Pisidia, and went into the synagogue on the Sabbath day and sat down.

And after the reading of the Law and the Prophets, the rulers of the synagogue sent to them, saying, “Men and brethren, if you have any word of exhortation for the people, say on.”

Then Paul stood up, and motioning with his hand said, “Men of Israel, and you who fear God, listen: The God of this people Israel chose our fathers, and exalted the people when they dwelt as strangers in the land of Egypt, and with an uplifted arm He brought them out of it. Now for a time of about forty years He put up with their ways in the wilderness. And when He had destroyed seven nations in the land of Canaan, He distributed their land to them by allotment. After that He gave them judges for about four hundred and fifty years, until Samuel the prophet. And afterward they asked for a king; so God gave them Saul the son of Kish, a man of the tribe of Benjamin, for forty years. And when He had removed him, He raised up for them David as king, to whom also He gave testimony and said, I have found David the son of Jesse, a man after My own heart, who will do all My will.’

From this man’s seed, according to the promise, God raised up for Israel a Savior —Jesus— after John had first preached, before his coming, the baptism of repentance to all the people of Israel. And as John was finishing his course, he said, Who do you think I am? I am not He. But behold, there comes One after me, the sandals of whose feet I am not worthy to loose.’

“Men and brethren, sons of the family of Abraham, and those among you who fear God, to you the word of this salvation has been sent. For those who dwell in Jerusalem, and their rulers, because they did not know Him, nor even the voices of the Prophets which are read every Sabbath, have fulfilled them in condemning him. And though they found no cause for death in him, they asked Pilate that He should be put to death. Now when they had fulfilled all that was written concerning him, they took him down from the tree and laid Him in a tomb. But God raised him from the dead. He was seen for many days by those who came up with him from Galilee to Jerusalem, who are his witnesses to the people. And we declare to you glad tidings — that promise which was made to the fathers. God has fulfilled this for us their children, in that He has raised up Jesus.

As it is also written in the second Psalm:

You are My Son, Today I have begotten You.’

And that He raised him from the dead, no more to return to corruption, He has spoken thus:

I will give you the sure mercies of David.’

Therefore He also says in another Psalm:

You will not allow Your Holy One to see corruption.’

“For David, after he had served his own generation by the will of God, fell asleep, was buried with his fathers, and saw corruption; but he whom God raised up saw no corruption. Therefore let it be known to you, brethren, that through this man is preached to you the forgiveness of sins; and by him everyone who believes is justified from all things from which you could not be justified by the law of Moses. Beware therefore, lest what has been spoken in the prophets come upon you:

‘Behold, you despisers, Marvel and perish! For I work a work in your days, A work which you will by no means believe, Though one were to declare it to you.’ ”

So when the Jews went out of the synagogue, the Gentiles begged that these words might be preached to them the next Sabbath. Now when the congregation had broken up, many of the Jews and devout proselytes followed Paul and Barnabas, who, speaking to them, persuaded them to continue in the grace of God.

On the next Sabbath almost the whole city came together to hear the word of God.

-- Acts 13:13-44 (NKJV)

Paul's sermon in Areopagus

So Paul, standing in the midst of the Areopagus, said: “Men of Athens, I perceive that in every way you are very religious. For as I passed along and observed the objects of your worship, I found also an altar with this inscription: To the unknown god.’ What therefore you worship as unknown, this I proclaim to you. The God who made the world and everything in it, being Lord of heaven and earth, does not live in temples made by man, nor is He served by human hands, as though he needed anything, since he himself gives to all mankind life and breath and everything. And He made from one man every nation of mankind to live on all the face of the earth, having determined allotted periods and the boundaries of their dwelling place, that they should seek God, and perhaps feel their way toward him and find him. Yet He is actually not far from each one of us, for

‘In Him we live and move and have our being’; as even some of your own poets have said,

‘For we are indeed his offspring.’

Being then God's offspring, we ought not to think that the divine being is like gold or silver or stone, an image formed by the art and imagination of man. The times of ignorance God overlooked, but now He commands all people everywhere to repent, because he has fixed a day on which He will judge the world in righteousness by a man whom He has appointed; and of this He has given assurance to all by raising him from the dead.”

Now when they heard of the resurrection of the dead, some mocked.

But others said, “We will hear you again about this.”

So Paul went out from their midst. But some men joined him and believed, among whom also were Dionysius the Areopagite and a woman named Damaris and others with them.

-- Acts 17:22-34 (ESV)