This isn't really a question we can answer. I know what you're looking for though.
We don't know how many child care facilities are in your area between where you live and where you work. We don't know how many small children there are in that area needing child care much less how many infants will be needing child care at that time either.
There's no way we can know how many infants there are in those infant rooms right now and when they turn 1 year old and move up to the next classroom. If a hundred babies are born in January and February then there would be an abundance of infants all fighting for the same few places. If there aren't many babies born at that time but all the babies in the infant rooms are all 6 months old then there won't be any spaces until they all turn 1.
Most parents want to have this all set up in advance so that's one less thing to worry about.
Can I suggest that you simply get a list of all the licensed child care options you'd have, such as those who don't take infants or that are just too far from your home, those can be ruled out until you have tried and failed at all the possible options.
Please call around to the child care centers and find out what their infant ages are expected to be and if they'll have any infants aging up to the toddler room when you'll need care.
For instance if your child is born February 15 and you get 6 weeks off then you won't need care for your baby until March the 29th. You'd be going back to work that Monday. So you would need to find a center who has some babies turning 1 year old at that time so they'd have an opening starting that week. If they don't have any March or early April birthdays they won't have any openings no matter if you're on their waiting list or not.
I don't know if I'm saying this well enough.
In Oklahoma 1 teacher in the infant room cares for 4 infants ages 6 weeks through their first birthday. As soon as they turn 1 year old they move to the toddler room. Walking or not. The reason this happens is because they can have 6 toddlers per 1 teacher so they make more money in that room. They might have a lower toddler room and a older toddler room. Those that aren't walking and able to do those things that they need to do to not get run over by running toddlers. The older toddlers would be more adept at running around and feeding themselves.
So moving kids out of the infant room is important so they can get more infants in but also so they can get more kids with one teacher for the charges.
I do think that calling them each and keeping some notes as to those who'll have more slots coming open at that time is a good thing. This will give you a timeline, sort of, so that you can figure out which ones to rule out or actually put down on your list of possible options.
There could be infants moving away, mom's deciding to stay at home, and other life changes that would take an infant from that room early.
So call each center and ask. I don't do home options simply because there is no one there to observe and know what they do all day. In home child care the adult can go take a shower, take a nap, talk on the phone all day, sit and watch TV all day, and more. I know they usually don't do stuff like that but I'd rather have the counters and check-ability that a facility offers. Plus if the teacher is sick someone WILL be there to fill in that the kiddo's know or are familiar with.
Overall I think it's way too early for anyone to know anything. But they may put you on their waiting list and then you may have a place when the time comes or not but still, they'll have you on it and can call you as soon as they have one.