If you aren’t on their list yet, you will be much, much farther out than April (think April of next year, or later). Get yourself on as many lists as you can, then suck it up.
You have approximately 7 choices for childcare (if you think of something I haven’t, let me know!):
1. One of you
2. Family
3. Nanny
4. Nanny share
5. AP (au pair)
6. In-home day care
7. Center daycare
Centers sometimes don’t call until your child is 2-3. In-home may or may not have a waiting list. An AP takes 5-8 weeks to get to the US, then may rematch for personality issues with little notice. A nanny will be in your home everyday, and may see things you don’t want anyone else to see; with a share, you have the obligation to schlepp your child to the other house, and none of the benefits of a single family nanny (laundry, cooking kid food, etc). The only ones that turn out as expected are you or family.
So, either make your peace with being an employer, or figure out something else. Good luck OP. Oh, and post in Employer on the nanny side, other hand agents will walk you through the legal logistics.