It is impossible to prove the age of the earth.
There is current evidence. We have test methods to analyze the evidence. We have assumptions and models to project from that analysis to a theoretical age of a rock, etc.... And then we can project from there to estimate the age of the earth. - But since no person was there and there is no odometer on the earth, it cannot be scientifically known; a logical truth.
Check the evidence and the methods and start adding up the assumptions that must be made to project the age of the earth. Then consider what is legitimate.