Record on Apple TV

If you mean the Friday Night Baseball games on Apple TV+, then no, recording or time shifting is not supported at this time.

Recaps of past games are available, though.

Not sure if full games eventually end up in MLB archives.

The Apple TV box itself doesn’t offer recording capability.

Select TV providers may offer “Cloud DVR” for their own Live TV broadcasts, in their own app, with storage on their own servers. That doesn’t apply to FNB games though, as those are Apple TV+ exclusive, and not available through any TV provider.

For games as provided through the MLB app, you’ll have to ask them for details on non-live viewing.

If you have ideas for improvement of the service, or changes that you would like to see, then leave feedback comments at: Feedback - Apple TV App - Apple