Well this right here shows it. You're willing to accept that the earth is so old when such ages break every scientific fact and even every scientific theory. It's simply impossible by its own massive weight and the sole reason it is taught is on consensus of a few pagans and atheists. They are not even credible sources for the age of the earth because they have only existed less than 300 years. Credible sources for the age of the earth is history. The Bible is history, it is not all the evidence, but it is a major piece of evidence that cannot be overlooked.
As for dating fossils to thousands of years old, yes, they can be dated that old. It can be dated with the historical record containing such creatures as living, evidence of the event which is needed to cause fossilization which is the Great Flood sent by God in the time of Noah, and the evidence of the ages after the Flood being exactly as the Bible and history says they are. Those are just a few ways, but are the hardest evidences.
Sifting through the evidence of history is a deeper matter, but it is not impossible. To examine this you can examine the historical record and how it came to be, archaeology, and the current conditions of the earth. All these and more can be used to prove history. Additionally this makes for a mountain of proof for the Bible as both part of history, but also as the all encompassing paradigm within which history itself fits into.