At that age, it is pretty much random. Some kids yes, some not and most of them are in the middle - sometimes yes and other times no. Their attention span is very small, so basically no child will play alone long enough for you to cook.
You cant really force it to happen in any case. Sometimes you cook while fighting the kid and that is that.
Small kids get bored quickly. They play with any given toy the same way I listen to songs: without stopping, until saturation, and then infrequently or not at all. Whether this will last 20 minutes or 2 hours or 2 days - it's kinda random. Even if you give the kid a completely new toy, chances are, they won't get interested immediately. Or even the same day.
Parenting is definitely 2+ person job. At the very least, it's a full-time job for one person.
Not making any judgement but I truly think that parenting is a two-person job.