How/when to have the conversation?

Welcome! Wow, this must be quite a whirlwind for you and your husband. There's a lot to unpack here, and many posters have done a great job getting that started. Some other things to think about:

-There is a power dynamic at play here that is touchy in terms of ethics. You imply her financial situation isn't great. If her best option for her and her child, financially, is to move in with you and your husband, that puts her in a bit of a quandry if she doesn't reciprocate one or both of your affections. She is also, possibly, emotionally vulnerable right now, and throwing this onto her, especially in addition to the housing, is questionable. It's up to you how you handle that ethical dilemma, but it's definitely there.

-Even if she does want to pursue a relationship, there's a lot to think about. What if she's only into you? Or, what if she is into you both, but later finds she's only into one of you (or is into one of you more than the other)? Or, what if one of you decided you're not that into her? It happens all the time--most relationships aren't forever. Does she lose the one of you she's into? Does she lose her housing?

-Even if she is into the whole threeway thing, if you're in the US, she'll never have the same legal benefits for her and her child that you and your husband do together. That may or may not matter to her, but it's worth thinking about and understanding. She also may want a "primary/nesting" partner of her own, like you would that impact things?

-Lastly, triads are one of the most unstable poly structures. It's not undoable, but there's a lot to think about that most couples don't. I highly recommend reading So Someone called You a Unicorn Hunter. While you aren't necessarily unicorn hunters, exactly, the points raised in this are pointedly relevant here, and should help all of you figure out what you might be dealing with in reality, rather than just in hypothetical fantasy.

It's not undoable, but it's definitely a challenging start. Let us know how it goes!
I had this whole big long thing written , and went back and read it again and it sounded like a bunch of horseshit. So I'll start over..
First, thank you greenacres, that was very insightful.You guys have given Jay and I hours of discussion on all the issues and topics you've mentioned and it has been so helpful in determining our intentions and different levels of comfort. Thank you all very much and for being so kind to someone who knows virtually nothing about this subject.
I'm going to talk to her this morning so I'll let everyone know how it goes.
Anymore suggestions I'm open for it.
Everyone has offered good ideas. One thing that hasn't been specifically addressed is that Bri just broke up with her bf/gf, it was messy, she's upset and reeling. I assume she was living with her ex, and that is why she needs housing.

It's never a great idea to try and date someone in the first stages of breakup grief. Much less having a couple hovering... almost like vultures, with this novel untried idea of polyamory in their heads and genitalia.

You live in the Appalachian mountains of Tennessee. I have a dear friend from there who moved up to Mass 2 years ago, and she has horror stories of how conservative it is down there. Or should I say, bigotry is accepted as the norm to a disgusting extent. She once went to rent a house, and the owner glibly told her she'd like it here because the nearest blacks lived way over there on the other side of the holler. Also, my friend is transgender, and when she came out, she lost no less than 3 jobs because of her gender.

I am pretty sure your neighbors and community would look askance at a married couple in their 30s moving in a very young 23 year old. (Her kid is 6 or 7? she had him at 16 or 17... hmmm...)

Her recent breakup, and her vulnerability as a very young single mom make her ripe for being abused. I don't mean to say you two would do that deliberately, but given that you are brand new to poly, inexperienced at its pitfalls, unaware of the red flags others have pointed out, this doesn't look great for Bri. You're white knighting her from a fantasy position.

And if she does move in, and doesn't return the love you feel for her, or returns it unequally, and one of you gets jealous, and she is dumped or chooses to leave, keep in mind how another breakup will again crush her, and now also your sons.

If it were me, and I cared for someone that much, I'd help her apartment hunt, job hunt, and at the most, juggle my finances to contribute to her rent for a year or so. It sounds like her life has been full of drama, having a child so young, and maybe no other friends or family to fall back on now that this relationship has ended. She needs to get on her feet as an independent woman, not immediately agree to take on a complicated relationship with a married couple when she has just broken up with her previous partner.

So, you both tell her you love her. Maybe she loves you too. But maybe it's all the rose colored glasses of infatuation and hormones. This could all fade in a few months. And then, where would she be? Worse off than before! You two would have contributed to making her life even worse, not better.