I can’t find anything about this dome in a google search

I gotta question your methodology here a bit, because just googling “firmament” will get you quite a lot of results and you don’t have to read very far into the actual Bible to come across the term (depending on the version of the Bible you read, different translations use different terms, sometimes I’ve seen “vault” used instead) its probably going to be right there on the first page of Genesis.

Now the Bible doesn’t exactly do a great job of describing the firmament. Coming up with an actual model for for the heavens and the earth kind of fell to various scholars over the years trying to make sense of it.

In general, if you take it literally, the firmament is normally interpreted as a sort of solid structure somewhere up above the sky that separates heaven and a whole bunch of water from the rest of creation and probably more or less resembles a dome above a flat earth. The exact structure of all of that will vary quite a bit depending on which denomination and scholars you listen to.

Even the word firmament should kind of clue you in that it’s supposed to be kind of solid, you can really go down a linguistic rabbit hole through all manner of English, Latin, Greek, Hebrew, etc. words with this but for the most part you’ll get the impression that you’re supposed to believe there is some sort of physical barrier there

Most of the mainstream sects have adopted somewhat less-literal interpretations over the years because obviously the science doesn’t support that interpretation at all.

But of course there are a whole lot of absolutely wacky Christian denominations (all of them are at least a bit wacky, but some really go the extra mile into the heart of crazytown) and even in the less-insane denominations some individuals pick and choose and come up with their own batshit interpretations of things.

Off the top of my head, I don’t know which sects stick to a literal interpretation of it being a solid dome, but I’m absolutely sure they’re out there, but most of them are probably not very mainstream, most of them are probably independent churches not affiliated or only loosely affiliated with any larger organization. And a lot of people who believe it are probably picking it up outside of any organized church and either coming up with their own interpretations or getting it from some wackadoo on the internet.

Trying to talk sense into her is probably an exercise in futility and I would not have even the faintest idea of how to go about doing that. If you do want to learn more about her specific beliefs though, a good place to start is probably going right to the source and figuring out which church she goes to and where she’s getting her info- what websites, books, YouTube channels, etc. and the best way to do that is probably just to ask her. Don’t try to argue with her and convince her she’s wrong, you’re not going to get anywhere, just get some links and recommendations, she’s probably going to view it as a chance to convert you and born again types are all about that, she’ll probably dump a whole bunch on you.