Jesus and the Old Testament
Actually this question is not accurate, as Muslims believe that the one who was on the cross had the appearance of Jesus.
So it may have happened that people were deceived and thought that the one crucified was Jesus (Peace be upon him).
Besides, if the point is historical evidence, then Christians need to give a historical evidence for the huge events that occurred in Matthew 27:51-53 talking about earthquakes,
And dead people raised.
This must have been an event which is greater than a man being crucified by the Romans.
For sure many people would have witnessed these huge events,
but actually it was only the writer of Gospel of Matthew who wrote about it.
Even the writers of the other Gospels mentioned nothing about these events.
When we look at what Early Christian sects said about the crucifixion of Jesus, we find that not all Christian sects believed that Jesus was crucified.
We find for example that
the Basilides who believed that Simon of Cyrene who was crucified; Jesus exchanged forms with him on the way,
And, standing unseen opposite in Simon’s form, mocked those who crucified him, and then ascended to heaven.
Also Gospel Judas which tells that Jesus told Judas that he shall sacrifice the man who shall clothe him.
Of course that doesn’t mean that Basilides or Gospel of Judas represent Islam, but it points to the diversity among Christian sects and heretics concerning the crucifixion of Jesus.
Now let’s examine the evidence Christians use to prove that Jesus was crucified.
The evidence is taken either from the Bible, or from the Jews, or from the Romans, or from Josephus.
As for the Bible,
when we look at the story of crucifixion in the four gospels, we find many contradictions in the story of crucifixion between Gospels as the way Judas gave Jesus,
The way Judas died,
the hour of crucifixion,
Who went to the tomb after crucifixion, it seems that everyone heard narrations and wrote them without making sure if these were really narrations or not.
This itself is proof that the Biblical evidence in the event crucifixion is not sound.
If two witnesses testified in a court with two conflicting testimonies, both testimonies are rejected.
So the Bible is not a reliable evidence here.
As for the Jews, the Quran itself testifies that they said that they killed Jesus, and this was because they hated him,
And tried to show that they were victorious over him, but actually they were not since God saved him, and made him rise to Heaven.
As for the Roman historians, the two ain testimonies were Tacitus who was born in 56 AD, and Lucian of Samosta who was born in 125 AD,
Both of them didn’t witness the crucifixion, but just narrated a hearsay.
As for what Josephus said concerning Jesus, there is a very serious doubt in authenticity of this testimony,
Even the Early Church Fathers didn’t know about it till Eusebius came in the fourth century and narrated it.
But at the same time, we find Origen -who was familiar with writings of Josephus- saying nothing about that testimony.
The conclusion is that saying that Jesus was the one crucified were only narrations that were transmitted between people,
and it lacks much accurate evidence.