So, I'm currently closeted and recently divorced (from a man), but I met a really awesome woman online and we are now dating. When in the dating process would you introduce a new girlfriend to your family, especially if you're not out and this would mean coming out?
That's great that you have met someone special! My advice would be to wait to come out to people and tell them about your new relationship when you and your girlfriend feel comfortable and ready. There doesn't need to be a certain timeline.
I would not introduce a person that I was dating to family until I knew the relationship was serious. Introducing a same sex partner to anyone pretty much informs them that you are not straight unless you go the route of stressing that you are just friends which might be offensive or hurtful to your partner.
For me, I would treat coming out and introducing a new girlfriend as separate things. Even if I thought that my family would take it well, I would prefer that they had accepted and adjusted to my “new” sexuality before introducing somebody to them, so I would put some distance between those two things. I agree with @QuietPeace that I wouldn’t introduce anyone unless the relationship was serious, but if I was seen with them by a family member or friend prior to that, then I wouldn’t want to have to lie about who they were to me.