Are there records of Spanish conquistadors encountering alligators in Florida or elsewhere in the new world? Would it have been their first time seeing such creatures?

The early modern era witnessed an explosion of interest in writing about the natural world. We have ample evidence of Deep Thoughts on things like alligators and mosquitoes. I've talked about how Europeans interpreted alligators, specifically, in some detail here:

[What did early European explorers in the Americas think of alligators?] (https://www.reddit.com/r/AskHistorians/comments/4r5ipp/what_did_european_settlers_think_of_the_alligators/d4ym1r8)