I agree God has not changed, but how He chooses to interact with His creation does change in different periods. However, I do believe a constant through all the different periods is we are only saved by God's Grace through Faith. Hebrews 11 is filled with superstars from the OT who were saved because of their faith.
I believe in different periods God gives man greater free will than in other periods. The garden, the time of Noah and in the Millennial reign I believe men are given more free will and in the end we show our depraved nature, which also reveals how great God's Mercy is because none of us are worthy on our own.
Man has always been saved by the grace of God, through faith. There could be no other way to be saved. Faith is the belief that what God says will satisfy His justice is what will satisfy it. ANd nothing else. But God has dealt with man differently on His terms, according to His plan, throughout history. That is plainly evident in the Bible.