There is much better historical evidence for the crucifixion of Jesus than there is for the vast majority of events of the ancient world. Whether you consider the extant evidence to be "historical proof" or not is in the eye of the beholder. FWIW, most academic historians would both object to the concept that we can be absolutely certain about any historical event (remember, history is a reconstruction of the past using sources - there is always going to be an angle, evidence, viewpoint, or frame of reference that we lack that can give us a better understanding than that which we currently have, even for the most well established events) while also be quite accepting the basic outline of the life of Jesus: he was born and raised in Nazareth, sometime in his late 20s or early 30s he began preaching apocalypticism in Galilee, eventually made a trip to Jerusalem where he was denounced by the local Roman governor as a traitor and executed.

The crucifixion of Jesus is attested in multiple, independent sources, some of which are from outside the fold of the nascent Christian movement. We have no credible reason not to believe it.

You might be interested in the FAQ, in which the historicity of Jesus is discussed, or the FAQ of r/AcademicBiblical, which also discusses this topic, but from their scholarly perspective.

EDIT: I'm now seeing that you're asking who is responsible for Jesus's death, not whether it's accepted as a historical fact, and I'm pretty sure that even the Bible claims it was the Roman governor Pilate, the immediate rise of Christian antisemitism which blamed the Jews for the act notwithstanding. It's been a long time since I've read anything on this topic, but to my knowledge, the only sources that go into detail about the responsibility are the gospels themselves. The outside sources state only that he was crucified. But crucifixion was a Roman punishment, not a Jewish one, so it's likely that it was the result of him committing crimes against the Roman state. Whether a figure like Pilate might offer the crowds a choice as relayed in the New Testament or not is not something I can comment on. There are experts on this sub in Roman history, so perhaps they'll chime in.