I have no experience in dating the age of the earth. I have no experience in dating the age of the sun. I have seen no evidence that anyone has such an ability. I have no personal experience whatsoever to confirm any of the secondary evidences that you might be referring to with regard to the age of the sun and earth. I have no reason to believe anyone on this matter until I see at least some compelling evidence.
Sounds like you have yourself a nice little safety net.
Look, many atheists will deny or have various doubts about the existence of God because they believe they have had no experience of God's existence. They believe there is no evidence of His existence. It could be that evidence supporting the existence of God does exist, but the atheist is quite simply not aware of it. It could be that some atheists have experienced God, but have since been convinced, for whatever the reason, that their experience of God's existence was not an experience of God's existence at all, but rather an experience of something else entirely. It could be that some atheists have experienced God, but they were not aware that they were experiencing the existence of God.
Thus the atheist perceives that no God exists.
Well, it seems that none of us are content to have no answers. We want answers. Why are we here? How did we get here? There must be a reason. There must be a cause. Whether we are right or wrong, we will come up with answers to these questions.
So we explore the universe for answers. We experiment. We test. We come up with models and hypotheses. If our models and hypotheses are not extinguished as a result of being obviously false, we cling to them until they are extinguished.
If a theory or hypothesis is not proven false, it does not necessarily follow that the hypothesis is true. It could be true, or it could be false.
Perhaps you believe the Sun predates the earth. Perhaps you believe that you have seen evidence that the Sun predates the earth. If so, I'd love to see it. I do not discount the possibility that this is true, but I am not convinced that it is true. Convince me.
It seems to me, that you too have yourself a "nice little safety net".