My DS always liked "busy boxes". I agree with Kate about exploring the world, if however those drawers he is opening are unsafe then busy boxes may supply one outlet for his curiosity and wanting to rummage.
A basket or old shoe box, he can decorate the outside with stickers if he likes sticking yet, and put a variety of items in the box. Not a 'set' of blocks or a 'set' of kitchen toys etc but more of a random collection. Mine had things like a paint colours chart from a DIY shop, finger puppets, train tickets, a small ball or squidgy thing, a set of picture cards, one music item, a few different textures items (small fabric samples or things like a nail brush), a little book, a pine cone...
He would go get his busy box and empty it out one item at a time and explore it, then the next then the next...until he had a pile of stuff then put them all back in. Would he like something like that perhaps?
It may also depend on what toys you already have at home and how you have them stored or set out. Some LOs like 'invitations to play' where you set things out rather than keep them in their storage boxes, and perhaps set out unexpected combinations or in unusual places as a surprise.