Millions of big-leaf maple seedlings come up most springs, only for the vast majority to vanish the same summer.

If, on the other hand you have a Norway maple seeding in there that could be problematic. Because on wooded sites at least these apparently do not tend to die off in this area. At least in certain particular locations that must suit them, resulting in them starting to take them over - as has long been happening elsewhere in the northern US.

I see that in the woods, but we water the garden areas in the summer. Last few years I've pulled hundreds. The ones I missed from a year or two ago have already developed a decent tap root and can take some pulling to get out. I'm really hoping it's a squirrel thang.

They're surviving in the garden because you're watering.

I've noticed in very recent years many hundreds of maple sprouts in the neighbor's yards (likely sourced from a nearby parking strip tree). These are coming up right in the lawns, not a likely place for squirrels to be burying seeds.

Yes, here in its native region big-leaf maple generates carpets of seedlings in season - wherever the seeds land.

I have always watered, but have only seen the explosion in seedlings over the last few years. I know the squirrels will bury some, but it looks like they're eating them. I hope I have hungry squirrels.