The problem here, as I see it - is that the YEC crowd are demanding that we ignore a huge amount of conflicting data just to accept their view. They offer nothing to support their position.
Someone might say "Well, it's the same thing with the resurrection of Jesus Christ and the virgin birth!"
But it is not the same thing at all. As I said, we have literally mountains of data to show the age of the earth to be about 4.5 billion years old. This forces us to re-examine the claims of the YEC advocate.
There is nothing however, in our natural world that would say a creative force, like the God of the Bible, could not and did not raise someone from the dead.
"Oh!" Timmy would say... "What about all of the people who die in the world today and fail to get up three days later? Isn't that proof from the natural world that people can't be raised from the dead?"
No. It's proof that resurrection from the dead is not a natural process. It says nothing about the supernatural.
"But then... why couldn't God have just created the world 6,000 years ago and made it look like it was an old earth? A "supernatural" miracle that defies all the laws of nature as well?"
Because then His imposition of false data into the geological and astronomical record would be a deception. Remember, on this question we have data from the natural world and we must engage and understand that information. We can actually see that the earth is more than 6,000 years old:

and
We're not like Thomas and the other apostles who were "blessed" because they did see and believe in the resurrection. We have nothing from the natural world at all that even speaks to the question of the resurrection of Christ.
When Jesus rose from the dead he bore the physical wounds - evidence - of His death and suffering. This is what in part, persuded Thomas to believe. Thomas had evidence from the natural world - the man Jesus Christ Himself - standing there as evidence. We are called upon to believe or reject this account based solely upon the evidence of reason and the Spirit of God.
The earth too, bears physical "wounds." Wounds which give evidence of a long age - much greater than 6,000 years. Just as Jesus challenged "doubting" Thomas to push his fingers into the wounds, we can actually touch the physical scars of the earth.
Accepting the overwhelming amount of scientific evidence for an old earth does not invalidate nor even challenge the miraculous works of God that are described in the Bible. They really aren't even part of the same discussion, though some folks like Ken Ham insist they are.
He doesn't even seem to notice that he has volumes of books and writings and an entire staff devoted to arguing against the natural history of the earth; yet not one soul tasked to address the scientific evidence against the resurrection. And why is that? It is because there is no scientific evidence that has ever been presented against the claims of the apostles.
There has been a long and often loud debate on the philosophical and theological aspects of the resurrection - but nothing scientific can be made against the claim. The age of the earth, on the other hand is an entirely different issue.