No dates given in the Bible and attempts to set dates based on recorded history may fall short of being accurate because we cannot know that every generation, or even the lengths of time of certain generations are interpreted correctly.
Additionally, (and I do not subscribe to a "gap theory" we can't really know how long God took for Genesis 1:1 to come about. No indication of time there. (FWIW, the "gap theory" presupposes a long period between Gen 1:1 and Gen 1:2.)
That the earth is likely "young" and not "old" is a given considering Biblical evidence, but there are issues that factor in from observation of the general revelation (the cosmos) that cause many to believe that our cosmos is much older than is typically assumed by Christian believers.
I'm not sure the age of the earth/cosmos is a point where we should be utterly dogmatic. Whether God took 6000 years, 10,000 years, a million years, or billions and billions of years (or made it appear that is what happened) we simply don't know because we are not given dates, and so we praise God as the God of creation, we praise God as the God who told us that He created the earth and all its contents in 6 days, and after that, we wait to ask Him in eternity.