I had the same issue. I was checking all over the internet to find a solution. Evry other thing on Peacock - including a live NBA game - worked fine.
I kept closing out of the app and restarting.
Eventually, at around the under 4 of the first half, I reopened the app and it ran a Spanish language ad for a colon cancer drug (because you should have to watch an ad before they stream you the content full of ads), and it started working.