WE deduce it as 6K years - the Bible never states that - which is why I rarely engage in "age of the earth" discussions, too many unknown variables.
God created the heavens and the earth. EXACTLY when that was? We can (and do) debate that 'til the cows come home, and it can be a fun exercise.
Does it change the central message of the Bible that we are fallen and can't get up (on our own), but God provides redemption for us in the Name of Jesus (only)?
How is the Bible supposed to state that? It can't. What the Bible does state is the linage and ages from Adam to Solomon. And it speaks of some historical figures and incidents from Solomon to Jesus. If we accept the Bible as literal truth, as creationists would have us do, then it's not hard to estimate the age with some accuracy at 6000 years. It may be 6000, give or take, but certainly not millions or billions of years as science tells us it is.
God created the heavens and the earth. EXACTLY when that was?
Day 1. "And God said, Let there be light: and there was light. And God saw the light, that [it was] good: and God divided the light from the darkness. And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day." Roughly 6000 years ago, as Ham would have us believe.
Does it change the central message of the Bible that we are fallen and can't get up (on our own), but God provides redemption for us in the Name of Jesus (only)?
No, it does not. But people like Ham want us to use the Bible as a work of science or of history, and not for the purpose for which it was intended.