I went to public school and public college, I was indoctrinated in the religion of evolution and zillions of years. It’s really no wonder so many people believe that nonsense, it was in all of their awesome dinosaur coloring books, it was in their favorite cartoons, the teachers gave them an F if they didn’t put 3.5 billion years on the test, the Crocodile Hunter said it on every show.
Let’s say the dating methods are completely accurate, you still don’t know if that rock was created with age already designed into it. God is capable of that. Your assumptions are so hidden from those you try to persuade they’re either hid with ignorance or with malice.
If you choose to believe in a god that purposefully deceives people about the natural world, that is your business. Again, however, so long as you don't pretend that such a belief is based on observation or the scientific process, and don't pretend that such a belief belongs anywhere in the pubic classroom, we have no conflict.
By the young earth assumption there are trillions of stars all within 6000 light years. That would be one hot and crowded sky :)