I'm relatively new to Meta, so I'm having trouble processing things in meetings as they happen, making them a substantial waste of time for me overall. I don't want to seem dumb, so I would to avoid asking a bunch of questions during meetings to make people explain what they just said. What can I do to make meetings more productive for me?
I don't want to seem dumb...
Flip this mentality! There's nothing wrong with seeming dumb if you quickly improve. Embracing being "dumb" means that you will grow out of that state much quicker. Of course, you don't want to derail the meeting by asking 15 questions or something, but I definitely think 2-3 should be okay. If you're new and you have a good team, people will definitely understand.
In terms of more concrete tactics, I heavily recommend my guide here on how to be more active in meetings: "How can I be more active in meetings and earn the respect of senior engineers?". In particular, try to "do homework" on the meeting beforehand, and the meeting invite doesn't have a clear agenda + relevant materials, don't be afraid to ask the meeting owner for them!
Lastly, there are a lot of tactics you can use to alleviate the anxiety around asking questions and making your team far more accepting of them, even if they're "dumb". For that, check out this discussion where I share a concrete example of how I would ask for help at Meta: "How do you overcome the fear of asking stupid questions / bothering people when you need help?"
A big Meta-specific hack is prefacing your question with "n00b question" - You can even use this if you aren't new to the company in situations like being new to a tech stack or when you have a suspicion that the answer to your question is obvious. It's pretty much a shield that takes an extra 1 second to type (pretty awesome ROI if you ask me!).
Do some prep work before the meeting. You can probably anticipate some of the questions you'll ask during the meeting -- now ask those before the meeting to someone who knows the answer!
Every meeting should have resources that you can dig into and learn about. If not, ask!
You should also be selective about which meetings you care about. When you're new, it's fine if you can't prepare for every meeting. But pick a few that will be high leverage and look up the terms, look up the people, and look up any historical context.
It's better to be fully in command for 1-2 meetings per week rather than half-heartedly know what's happening for every meeting.