I agree that we need a body to establish existence. That is the most direct way without an incredible streak of good luck in finding a body, skeleton, or fossil. Gigantopithecus was defined and accepted from finding a few teeth and a jawbone. We have nothing like a complete skeleton so for all we know it might be BF or an ancestor of BF. We certainly have not established a familial line leading up to Gigantopithecus either. You don't suddenly have a giant ape without a familial line of smaller ones leading up to it. All of those ancestors are missing in the fossil records. So it is hardly surprising that BF ancestors are missing from the fossil records too.
The Pleistocene fossils you mention are not in BF habitat. I can not recall a single BF sighting in the Willamette Valley. BF would not leave the safety of the mountains. The mastodons and other finds are in what used to be grasslands between the Coastal Range and the Cascade Mountains. The same areas inundated by the Missoula floods during the last Ice age and possibly the reason for finding those mastodon bones and fossils there in the first place. And the fossil beds associated with inland lakes in Eastern Oregon and Washington are in an arid region that is also not forested and likely BF habitat. No BF sightings in those arid regions are reported in the present day. . You basically cannot expect to find bigfoot fossils or bones where it has not lived. If humans migrated to North America towards the end of the Pleistocene one would expect that BF did the same thing since there is no history of human or prehuman ancestor habitation in the Americas before that. So not only geography but time would have prevented formation of fossils in the Pleistocene in the PNW. . Since the Pleistocene started about 1.8 million years ago, that far back we could have had common ancestors in Africa and as those would be smaller we could not make any association with modern day BF.
It could be that BF beat humans to North America. We have no idea without something to date their arrival. But once humans did come, there went the neighborhood and BF adopted their present human avoidance tactics which they probably used when they cohabitated with humans on the Eurasian continent. Human history is one of killing everything that moves to eat and that probably includes BF.
If I were to look for BF fossils or bones I would look in the Ohio and Southern Illinois area where BF sightings are common now. The soils are not as acidic, the rivers in the Midwest flood nearly every year, and so bones of BF trapped by flooding might be possible to find washing out of river banks. Of course a tree climbing creature is going to be hard to drown in the first place.