I'm a SAHM to a 4 year old boy, also an only child. He attends pre school a couple of days a week, the rest of the time it's just us.
Structure is key for us, breaking the day down into smaller components. Being out and about is much easier.
If I have things to do, he wants to be in the same room so I set him up with some toys but expect him to get on with it. He uses his imagination far more when I leave him to it.
I balance time focused on him with time for me to get things done.
He comes me with to run errands, food shop etc.
We have a rotating list of things we do out and about as just going to the park is a bit samey for both of us. So some free things (park/walk/watching trains at the station for example) and other things like national trust, farm, softplay, big shopping mall/ikea, adventure playground. Summer is easier as we can spend a whole afternoon in the garden.
At home we might bake, build a train track, colour, read, throw a soft ball, play board games.
Structure and fresh air is the key though.