Welcome to the neighborhood! We moved from DC a few years ago.
Wonders Daycare (two locations: one in Chevy Chase and one on Bethesda) is terrific, but I’m not sure if there are openings. Another one to check out that people seem to like is Children in the Shoe, two locations across from one another on East-West Highway. Both use the Creative Curriculum. Wonders is a nonprofit, and the Shoe for-profit, but I think they charge around the same.
Most of the preschools around her are part-day and even with aftercare did not cover a full workday, so those didn’t work for us. That said, there are a lot of nonbelievers who send their kids to the church-based programs such as at CCUMC.
Good luck!