Wanting to get myself in the best possible shape for Iceland, I got my second covid booster today. That gives me three weeks before leaving for it to kick in fully. As of today you don’t need a covid test to fly USA-Iceland but Iceland-USA does require a within-48-hours negative test to leave.
A friend was coming back from Ireland a couple weeks ago, tested positive upon departure, and was stuck in a hotel for five+ days until he tested negative. It can happen, no matter how careful you are, bang, you’ve got covid.