As they say anything is possible, but not necessarily ADVISABLE. (You may be pulling your hair out very shortly.)
I am going to leave others to tell you how, to pull off “dancing on this log”- but CAUTION you, I would NOT attempt to, not only housebreak, but carefully socialize (before 16 weeks) and begin really necessary obedience training (in a puppy) AT THE SAME time……… as getting your child to use a potty *consistently*. The puppy MUST be under good control and completely free of any likelihood to nibble or nip; since a two yr. old will be on FACE LEVEL with it…… a LOT.I would NOT EVER get a puppy or dog in these circumstances, WITHOUT a fenced yard. If all hell breaks loose, had you a fenced yard – the puppy could go OUT the door & you could carry kiddo straight to the potty. WARNING: Staffies & other bully breeds are normally very HIGH ENERGY and require a lot of daily exercise, so I hope you have THAT figured in to your daily routine, as well. Right now your puppy still needs a nap, but NOT for much longer…..if it becomes typical, you will have a non-stop, ENERGIZER BUNNY.(I will have a padded room and straight-jacket on stand-by, for you.)