Omphos means navel. There has been speculation about whether God created Adam with a navel or not, given that it would have no function for Adam why would He?
Omphalism refers to the belief that God created the universe 6000 years ago with an appearance of great age.
I ponder what is the difference between an infinitely powerful creator creating something with the appearance of age and the thing actually being old?.... A difference which makes no difference IS no difference.
Further omphalism is scientifically indistinguishable from a rival contention that the universe is 5 minutes old, and God created us all 5 minutes ago with our memories intact. Such claims are essentially worthless because they cannot be tested.
Why would anyone trust or worship a trickster God who for unfathomable reasons created the universe to make it look old when actually it wasn't?
OK, I suspected you ment some take on young earthers like myself.
So is the theological problem the one where God says He created something but gives no way to prove it? So if God said He created Adam from the dust and even if there were people there to examine Adam he would seem to be older though he was just created? Therefore the appearance of age is a lie which God would never do? Ditto for the universe.