The cross in prophecies

There are no prophecy that refers to any cross-like symbol. Instead, the prophecies foretold about the suffering of Christ but never mentioned in what form he would be nailed to.

Archaeological evidence

From the archaeological evidence, we did found nails driven into skeletons by the Romans which proof that the Romans did nail people onto wooden structures or trees, but we do not know exactly how the structure looked on which Jesus was nailed.

Both John 19:17-18 and the Jewish historian Josephus, who lived in the first century, used the Greek word stauros which means "a stake or an implement of capital punishment". In older Greek texts, "stauros" means "pole".

Bible translations

However, because many translators commonly translated "stauros" as "cross" in the Bible, many were lead to believe that "stauros" means "cross", but that is circular reasoning and does not proof anything.

The Septuagint is the Greek translation of the Hebrew Bible, written by 72 Jewish scholars at the request of Ptolemy II Philadelphus, king of Egypt. This translation does not contain any references to "cross" symbols or that the Christ will be "crucified". It only states that Christ will be:

pierced for our transgressions; ... crushed for our iniquities; -- Isaiah 53:5 (ESV)

Even Peter said:

He himself bore our sins in his body on "xylon", that we might die to sin and live to righteousness. -- 1 Peter 2:24 (ESV)

"xylon" is the Greek word for "wood" or "timber" which could mean "tree" (as translated in the ESV, Berean, KJV, NKJV, ASV, ERV, ISV, Majority, NET, Webster, WEB, YLT, etc.), but could also refer to any general "wooden" structure (as translated in Godbey, Smith) which could be a "cross" (as translated in NIV, NLT, NASB, AMP, CEV, GNT, NRSV, etc.)

Identity

People groups tend to seek symbols or logos to identify themselves. The cross (🕇) is a symbol that identifies Christians. However, besides the modified translations, there are no evidence that Jesus or the apostles used the cross as a symbol as their identity.

Jesus said:

A new commandment I give to you, that you love one another: just as I have loved you, you also are to love one another.

By this all people will know that you are my disciples, if you have love for one another.

-- John 13:34-35 (ESV)

God's children is not recognized by a crosses, special culture, membership, dress code, hairstyle, facial expression or such, but instead they are recognized by their unselfish love for one another.

Ancient Tav

Some Christians are quick to point out that the ancient Hebrew letter "Tav" used to look like 2 crossed sticks which could look like a cut-down Christian cross if you use your imagination.

Today, the modern Hebrew letter "Tav" no longer looks like a cross.

The ancient Hebrews definitely did not had the Roman crucifixion in mind when they invented their language's letters.

Remembrance

Jesus never worn, or handed out any crosses.

Instead, Paul wrote that communion should be our remembrance of Christ's bread and new covenant:

For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, “This is my body which is for you. Do this in remembrance of me.”

In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.”

For as often as you eat this bread and drink the cup, you proclaim the Lord's death until he comes. Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty concerning the body and blood of the Lord.

-- 1 Corinthians 11:23-27 (ESV)

• The bread symbolizes righteousness and fellowship with the Father, the Son and fellow believers.
• The cup symbolizes the new covenant with God that seals our reconciliation with Him by the forgiveness of sin.

I doubt that Jesus would like to be remembered as a shameful weak victim of a Romans crucifixion who is about to die. It would glorify Jesus more to remember his accomplishment to reconcile us with God and to remember his love for us.