I think the word arbitrary doesn’t mean what you think it does.
Differing definitions is a possibility. I understand you to be satisfied with the numbers geologists propose. That's fine. There is much about their work I appreciate, but I feel in no way obligated to accept whatever they propose. That would be arbitrary, too. Quantum mechanics is creeping up on a reality that makes a billion year proposition as relevant as a nanosecond proposition, all of which is very much in accord with what the biblical text teach regarding the Creator.