Could Giant Anteaters survive in Pleistocene Florida?

I’m doing a light speculative series involving Pleistocene conditions and Megafauna surviving into the present, and there’s a few speculative editions, mostly involving animals migrating into the state, including Elk and Dwarf Pronghorn from NA, and Mixotoxodon and Coati from SA. There’s even a small Terror Bird and northern species of Rhea

But one animal I’m considering adding is the Giant Anteater. They migrated as far north as Mexico during the Pleistocene, and I figured id have them continue migrating north into the Southeastern United States.

The habitat is about right (woodlands and grasslands), but I’m worried they won’t find enough to eat, unless they’re hardier than i imagined or can break through trees to get to bugs.

So is it possible?