You can, people do do it.
You will need excellent robust child care and this will depend where you live (back up nanny/ child care agency which provides a back up if the nanny is sick) as not everywhere is covered by robust childcare solutions. Our area is not, lots of childminders and nurseries but hours are generally 7.45-5.30, 7.30-6 is absolute gold dust round us and as a result the child minder and nursery who offer it are ££ and have a waiting list, to get in the nursery you need to put name down at birth and pretty much commit to full time hours as they are so in demand.
You will need a DH who is happy to be an equal partner, for your career to fly you will need to show that DC illness/ sickness is shared burden. Even if that means DH is unpaid.
You will need to be very good at sharing the mental load of DC or employ someone who will take almost all that on for you. You are looking for much more than a nursery/ childminder you need a nanny.
You will need to outsource the housework to prevent burn out- cleaner, ironing etc. Could be easier to look for a housekeeper.
I know people who have done it, they have an au pair, live in nanny and someone who comes and batch cooks for them. I know another couple who live in a multi generational home and the grandparents take on all the child care and house stuff (it is their traditional culture to do this and in return the DC look after them in old age until death). I also know people who have 1 SAHP or very very part time job.
We opted for the SAHP role until DC get to school then I will return to the family business during school hours. I have chosen this and DH values this choice. I have never been a really ambitious career person and always wanted children and SAHM works for me. If it didn't work I would have gone back fully supported by my DH and we would pay for childcare.
You have to choose what works best for you and if you want a career then you go for it.