"Evidence," at least as it is understood in modern times, may not convey the proper understanding. "Fact" or "events" or "reality" might work better. Even in the OT, God appeals to those who were present for His rescue of His people from Egypt to tell the next generation about what they saw. He makes the same appeal regarding the events at Mt. Sinai when He established His covenant with Israel. By working these signs very publicly, God establishes that He is not like the false gods people worship.

There are other examples, as well, such as God commanding Joshua to build a monument of rocks in the middle of the Jordan river as the Israelites crossed it on dry land (God parted the Jordan as they entered the Promised Land, just as He parted the Red Sea when they left Egypt) so that future generations would know what had happened.

I agree that when all evidence is laid bare God's existence is known. Nevertheless, it is history and the "evidence" that depends upon God. He is the primary cause in every event. For this I would say that we begin where the Bible begins: in the beginning God... There is no question. The burden of proof rests not on the Christian.