The great thing about television, is that "live" is a flexible concept.
The playback software could happily play 10 seconds ahead of what's actually on the screen, and have plenty of time to translate like that.
In the same way that we sometimes put delays into live events to allow the subtitling systems breathing room.

It's already a thing with near-zero delay. MS Teams does it (dunno about the translation) and the QSMP Minecraft server has a bunch of livestreamers from different countries who use it for realtime translation.

[EDIT: Live demo from today. Shit's impressive.]

What actually happens is that the current sentence gets "corrected" several times as you keep speaking. It's a bit jittery and if the word order differs significantly then the translated sentence might be a bit wonky for a few seconds, and there are a few misses but overall it works really well; at least well enough that people who don't speak each others' language can have a conversation in their native tongues with essentially no more delay than reading speed. I can easily follow a livestream in a foreign language with the live subtitles (which was not the case a mere 6 months ago for any language other than English).

Live shouldn't be used in a home setup anyway unless for something where interaction is required, like a teams call or twitch stream. Anything else can take a delay for the sake of preserving the meaning.

It doesn't have to be live as in with the player but I imagine the audio could be loaded into the program simultaneously and have it produce cc for the entire movie as you watch it

I don't think I would use this actually, because I don't see how an AI could capture the performance. I'm a sub over dub guy anyway, but at least someone making a dub has a sporting chance to make an interesting performance.