Out of curiosity, how does your girlfriend react if you just start talking to her without asking attention? (Reason I ask, occasionally I think I might be on the spectrum, and my SO has a habit of just starting to talk to me. Most of the time I miss the beginning, which annoys to no end my SO...)
Different from the person you replied to, but my wife is also autistic, and she does the exact same thing (both needing for me to ask for her attention multiple times and not hearing anything for the first little bit if I don't get it). It used to annoy me but then I realized that was a silly thing to be annoyed about, and I just had to change my mode of talking to her.
I think it's a nice thing to do, in any occasion (except when it's urgent) (friends, coworkers, family,…), to call someone (by saying their name or with a gesture, or something), let them take time to focus on you (and possibly write some note so they can come back to whatever they were doing easily), and then speak.
I know multiple people who need some time to switch to you when they are focused (either they can't listen before, or they can but would lose their track). And that's fine. And they are probably not autistic. They usually don't need to be called multiple times though, that would be a bit annoying but hey, what can one do. I'd probably get used to it.
I don't usually need time to switch to someone interrupting me but certainly don't like it when the other one assumes I'm listening before I showed I'm listening.