“...I need no other proof of the world’s age other than what God wrote in the Bible.”
What did God write in the Bible about the world’s age?
That he created the world in 6 days, and took a rest on the 7th. He then gives us a full account of people’s genealogy, from Adam to Noah, Moses, and onward to Christ. Putting the ages + time of births together on a time line allows one to accurately calculate the amount of time during history Before Christ.
And yes, God did not physically write the Bible. Men did through His inspiration. “All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work.” - 2 Timothy 3:16-17