My daughter was born in August 2022, in Ontario. I had her birth certificate within a week(we ordered all three types of birth certificate just to be safe).
I got her Canadian Passport, and that process was only about two weeks before I had it back but I just used her birth certificate to cross at the land border to visit my husband.
He had to contact the consulate in Toronto to schedule the CRBA appointment at this TorontoCRBA@state.gov address. And they sent emails back and forth with my husband and set an appointment up and gave us a list of things we needed. I tried to see when we initially contacted them but I can’t remember. I want to say we contacted them in October, and had an appointment first week of December. And then we had her new US passport about a week later, and her other CRBA paperwork.
I just did my visa interview in Montreal and I just got notice today my passport will be back tomorrow. So that’s less than a week since my appointment. I was DQ’d in April, got my interview date in July, did my medical in Toronto, and should be all done soon.
Based on your timeline you should have plenty of time to get your little ones documents in order before your visa expires. Even better for you because you’re already in Toronto for the CRBA.