First, congrats to you and your wife on your baby! I’m not sure what you’re trying to schedule the same day as you try to register the birth of your child, though. You have to get through the NVC stage before you deal with the embassy at all for your wife’s visa/green card. They’ll ask for an I-864 affidavit of support and some other supporting docs, then they’ll review them, then they’ll forward your case to the embassy with a scheduled interview date for your wife for her CR1/IR1. You can reschedule if you need to but given current timelines, you’re unlikely to see an interview for at least a few months yet.
Given the fact that you two have a newborn to look after though, you might be able to make the case thet separation for a long time (you in the US and your wife/child in the UK) causes an undo burden onto your US citizen child (as newborns need a lot of care) in order to get NVC to expedite your case.
Look up the process for the NVC expedite request either on VisaJourney or just google around. They’ll have the embassy look at your situation, and if the embassy approves your request, NVC will prioritize review of your documents and schedule an interview for your wife’s visa at the earliest possible date.
All that said, this thread is about the process of getting a spouse green card when the US citizen petitioner lives in the UK and the I-130 is filed with the State Department at the London Embassy under exceptional circumstances, so I don’t think this thread is where you should be seeking advice. I’d recommend making a separate post asking about your situation specifically.
