The Qur’an is revelation from the God who was there, which is a better source than any human record. Doesn’t saying it offers no first-century sources assume it’s a seventh-century human text, which is the point in dispute?

This is the crux, and it should be said openly. From a historian’s standpoint, the Qur’an is a seventh-century document and its claims about first-century events are assessed as such; from a Muslim standpoint, it is divine testimony. The argument here is historical and cannot settle the question of the Qur’an’s inspiration. What it can do is show that if you ask the historical question, the earlier evidence points one way. A Muslim who accepts the Qur’an’s inspiration on other grounds is not refuted by history alone, and the force of this claim depends on a willingness to weigh historical evidence about what the Qur’an asserts.