I am having trouble watching live New York Mets baseball tonight on my app

Apple, MLB announce July “Friday Night Baseball” schedule on Apple TV+ - Apple

Friday, July 14 7 p.m. ET Los Angeles Dodgers at New York Mets

Friday, July 14 7 p.m. ET San Francisco Giants at Pittsburgh Pirates

I think the game started more than two hours ago, but it should be available for the live remaining time, as well as rewatching from the beginning.

Watching the Friday Night Baseball games requires an Apple TV+ subscription this season. Do you have that?

Try this link in the browser on e.g. iPad or Mac. It should offer to re-direct to the game in the TV app for a better experience. You can also use Search to find the MLB overview or search by team in the Apple TV app on any of your devices.

“I am having trouble …”

It is not clear which part is not working for you. Can you find the page for the game? What happens when you click the [▶︎Watch] button?

Try typing Dodgers at Mets in the Search box.

That gets one result for me, and I believe the game you are looking for. That should have a Full Replay (full game ~ 3hrs) and a Recap (3 min condensed version) available.