All things considered that stone would have been set at about the time the Treasure Fleet was drifting about.
Obviously one of those very large Chinese ships would not have made it up the Mississippi, but they did have smaller boats with them and carried all the technology they needed to make more of them no matter where they traveled.
Regarding leaving behind some DNA, that'd been fairly invisible in the local North American Indian populations of the time since, for the most part, they and the Chinese shared a common ancestry.
So, absolutely no proof it’s Chinese. I swear, they remind me of Chekov on Star Trek.