This may be your experience, however I have extreme doubt that these are anything but learned behaviors. There is nothing intrinsically masculine or feminine about sticks, dump trucks, strollers, or dolls. They are just objects, and for the majority of human existence the latter three didn't even exist in their current form.

All knowledge of these objects, what they're used for, and who uses them were learned from societal influences. A kid doesn't have to care about social norms to tell that most people they see playing with sticks or driving dump trucks are men, and most people they see pushing strollers and playing with dolls are women. It's like that from out in the park to within picture books.