new baby childcare

We're TTC but when we do have a baby can't afford to quit our jobs. It seems like most daycares are open 8-6 style hours. I work 6-2 and that's not a flexible schedule. Any tips on how to make this work, would I be looking for private sitters, etc? Are there 24 hour daycares? This is probably the only detail I haven't been at peace with. 
Additional/ we are both in the medical field so the hours aren't very flexible. Dad is on call at least one day a week and some weekends, he doesn't get to decide which ones. I have had my job for 10 years and would hate to quit because I have a retirement and I don't think I'd be happy not being able to support myself a little, plus retirement. We are not married so it would also limit my healthcare benefits to quit my job. 

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