Affordable childcare options in Chicago (update)

My hours will change when I find a job and childcare is my biggest worry. I have read a lot of threads here and could not find my exact situation. I looked into subsidies but the forms are long. How long did subsidies take?

Our county's childcare assistance took about 10 weeks to approve, but it covered most of the cost.

Libraries and community centres run free activities that gave me a couple of hours.