It depends. I was up and about within hours of my second baby and found him really very easy, but recognise that I was pretty lucky. Certainly my first baby was harder.
In part it's just the immense shock of realising that you have a tiny being dependent on you 24/7 who you really can fuck up big style if you don't get it right. I know you know that already, but personally I found that it didn't really sink in until after the birth.
If you have a hard labour and an em CS, then perhaps get a wound infection, it could be 6 weeks before you start to feel human again. By which time the baby will be at maximum demanding level.
You might have a baby with colic, in which case you may not be physically able to put him/her down for more than a few minutes. Try eating one handed, going to the loo one handed, making a cup of tea one-handed.
If you are establishing breastfeeding it may go swimmingly, or you may have hour-long marathons of trying and failing to latch.
Even if you have a fairly easy baby, it's not that easy to switch off. You may only have 20-30 minutes before they are up again for the next feed/wind/poo or whatever, so that means in practice by the time you have gone to the loo and had a cuppa, and just started to fall asleep, they are up again and ready for the next round.
Also they usually feed every 2 hours round the clock for about 30 minutes at first, and they usually poo with every single feed, which means they require a nappy change which takes about 10-15 mins at first. So JUST feeding and changing takes up 45 minutes every two hours, and then you have an hour and 15 minutes in which to: Sleep, eat, bath, dress, pee/poo, cook, clean, washup, do the huge mound of washing newborns mysteriously generate, talk to your partner, feed the endless stream of relatives who will descend on you... you get the picture.
Do come back and post when your little one is here and tell us how much spare time you have!