Ovulation after BC

Hello, I was reading through similar questions but my husband and I are going off BC soon and I'm trying to decide when to stop. We want to TTC at the end of May as we have a big hiking trip coming up that I would rather not be pregnant for.

I'm trying to decide if I should stop my BC (Tuesday 4/25) and use a backup method for the month of May and allow my period to return on its own? Or complete one more cycle on BC and start TTC immediately after stopping BC? Is it possible to ovulate right after stopping BC? I don't want to prolong TTC but trying to stay hopeful that i could ovulate and we could get pregnant soon after stopping BC. Thanks in advance!