I don't have children, so please take what I'm saying with a pinch of salt.
I think it partly depends on what your beauty routine was like before the baby. If you had a very long routine before the baby came, then you will probably need to think of what the bare minimum you "need" is, and work with that.
For example, I would say that my beauty routine is very short and simple. Teenager face wash (thanks grease genes), followed by a small amount of benzoyl peroxide (as above), then a bit of eye cream, then some number 7 moisturiser. That takes a grand total of...two, three minutes?
Make up wise, try and find products that work well alone, and don't need a lot of blending (like heavier foundations, powder blush) or very careful application (liquid eyeliner, strong coloured lipsticks), and go for things you can basically put on without much fuss (I'm always recommending the clinique chub sticks for lips, and I often use them instead of blusher as well).
I don't wear foundation really, but I'll use clinique's city block (tinted moisturiser basically with a high sun screen) or clinique's CC cream (as above), a bit of clinique concealer, eye brow pencil, lip balm, mascara, and some eye liner if I'm feeling glam. Again, it sounds a lot but I guarantee it can all be done in three minutes or less. So that's just over five minutes total start to finish.
Because it's so light it will look fine if it "wears off" a bit throughout the day, rather than a full face which will inevitably leave you resembling a drag queen.
On rushed days you can probably get away with just the preparation (moisturiser etc), a few bits of concealer, a tiny bit of powder on nose and shiny areas, and some creamy blush. That's one minute!
Also try and go for really easy hairstyles. If you've got long hair, put it into a neat high ponytail, or a bun and it should last all day whilst still looking polished.
Most of all, I think it's about accepting that you deserve the few precious minutes to actually do this, to keep your confidence from sliding.