A sharp increase in Carbon-14 would be visible for a few thousand years.
The rest of the elements released by nuclear testing? Not so much. Cs-137, and Sr-90 both have half lives of about 30 years. That means that after about 300 years, they’re both completely decayed into their daughter products.
Now, Cs-137 decays into Ba-137, which is stable. It’s also naturally occurring as about 11% of all Barium.
Sr-90 decays to Yt-90, spends a few days as such and then decays to Zr-90, another naturally occurring isotope. Zr-90 is a bit over 50% of all naturally occurring Zirconium.
They’d bring back company script.
And then get eaten by bears.