I misunderstood - I thought the problem was wanting to get on with things/spend time with the baby without him around in the mornings (from the wishing for him to have a 9-5 job).
Not that the baby needs to stay with Dad for another few minutes until she's had a shower (or if a morning one isn't wanted, putting baby into the car seat so it is perfectly safe on the bathroom floor whilst she has one in the evening).
At the same time, as he makes his breakfast, it wouldn't kill to make two portions, rather than her relying upon a sugary snack. And it's simple enough to eat or drink coffee with the baby beside you. Admittedly, it can take a little while to get used to eating with one hand, but it's doable.
It's handy to make a batch of bottles up in advance so they are just taken out of the fridge and warmed up as needed during the day.
And as babies get older, they usually get happier being laid down, rather than needing to be held all the time. Or, if not, a sling makes it easier to carry on with the things that need to be done whether there's somebody else there or not.
It's easy to slip into not even asking for things to be done differently and quietly seething about it when the other person doesn't instantly know what would help.
Other than that, if it's in any way possible, I'd say that a dishwasher is an essential part of reducing mess in the kitchen - and it's not hard for anybody to load one as they go along, as it gets the things out of the way instantly.
My routine when the second came along was;
Deal with baby, get dressed. Initially was about 5am, but gradually moved to just after 6.
Sort out pets. (at this point, the ex would be getting up and sorting himself out, whether it was for work or the gym).
Get older one ready for school.
Chuck stuff in dishwasher.
Put baby in buggy.
Walk to school.
Walk back, sometimes via the shops. Baby usually asleep by the time I got back, usually stayed asleep whilst carrying buggy up five flights of stairs, so left in there.
Have breakfast/brunch, chucking plates, etc, straight into dishwasher and switched on.
Get on with 'stuff', including sterilising bottles once I started switching to them at 3 months.
Baby asleep again from about 1.30pm, sitting down for a bit/having lunch/whatever.
2.30pm, start school run.
Back at 3.45pm.
Tea at 5pm.
Oldest for bath, story and bed at 7pm. Ex was usually in by this point, so dinner was put on whilst he did fuck all changed his clothes and watched telly.
Once eldest in bed, scoot around the kitchen with baby nearby.
Baby cuddled whilst watching TV.
Baby bedtime routine. If still wakeful, taken into the bathroom with me.
Worked well for me - and when I went back to work part time when she was 4 months old, it worked for the two days I had off, too especially once the ex fucked off and I went back fulltime
Admittedly, the second was an early summer baby, so there wasn't quite such a huge rush all the time and the weather was generally a bit brighter and nicer, but the rain cover and waterproof jacket saw plenty of use from September onwards.