It isn't the baby the takes up the room, it's the push chair, the changing bag, the massive car seat, the toys etc etc etc.
When my daughter was a baby we struggled with my focus, we could get everything in alright but then there's no room for shopping etc.
After 6-9 months or so when your baby is a bit older he will be able to sit upright in a normal push chair so we've now got a small fold up one for the car, and you aren't ferrying around loads of nappies and bottles / changine gear etc, we now just use a small ruck sack with a couple of nappies and some snacks.
So for the first few months you might find you will struggle, but as baby gets older you will be carrying around less and less.