(emphasis added)
Let's just look at that bolded assumption there. It's strange that you picked it out as a problematic assumption, because as far as I can see, that assumption also forms the centerpiece of YEC standard operating procedure.
Take, for example, the claim that human and dinosaur footprints have been found together in the Paluxy River. What is the claim here? The claim is that some time 4,500 years ago, a human and a dinosaur made footsteps side-by-side in some soft river soil, which then fossilized into today's record.
Note straightaway the huge amount of "anti-supernaturalism" involved. The obvious assumption is that during those 4,500 years, nothing supernatural has disturbed the fossilization process, which has proceeded by entirely natural means, with no trace whatsoever that God intervened in any way. Also, the initial process of fossilization assumes that clay acted like natural clay, that dinos and humans have weight (when any number of miracles could have caused them to levitate, or caused a human's footprint to look like a dinosaur's), that they had the time at all to lay down footprints, etc.
Any piece of "scientific evidence" for creationism assumes precisely that God has not acted in the past in supernatural (unnatural) ways upon the evidence in question between the time of its deposition and the time of its examination. Isn't that a pretty heavy accusation to bring?