My oldest is 3 and has since he started crawling tried to play with models, paints etc. The way I dealt with this so far is pretty easy.
First, magazines, rule books and the internet are your friend. My son has an old white dwarf that he constantly has me reading to him. He also regularly has me go through all my rule books with him. Not always reading the text but just talking about the pictures. The same goes for the net, we spend hours just looking at pictures of mechs, robots, spaceships etc.
Now when it came to models I at first let him play with metal sternguard models. These were great because he couldn't really hurt them and he enjoyed them immensely. To the point that he now roams around the house claiming he is a space marine or a crisis suit hunting for tyranids. When he was about 2 I gifted him the mechs from the battletech 25th anniversary starter. This is when he went into overdrive.
He carries at least one of these everywhere, usually a hunchback or cyclops and will happily tell anyone who listens about them.They have also been rather durable with mainly the smaller ones needing occasional re-glueing of weapons. He loves them so much we often read the different manuals. He can now name all the mechs in the starter and will tell you whether or not they are fast, jump capable and there class. He also regularly uses his legos and duplos to build his own mechs or towns for them to fight in.
Most recently he has moved on to playing with DW and FSA models. He does large ship battles using a simple dice game we play with d6. In the game we role a d6 whoever gets higher wins. He has applied that to the different ships on his own with the smallest getting 1 die, medium two and large ones 3.
Now lets talk about the benefits. For me the biggest benefit is his language skills. My son is multilingual and his primary language isn't English. This is an interest that has massively expanded his English vocabulary and improved his sentence structure, never mind the improvements to his basic math and counting. This is why I happily encourage him to play and talk with me about models, even though my wife isn't thrilled about it. Though it also causes some problems, for example I cant really let him paint yet. Even though he begs too. The other problem you may run into if you don't securely store your models, this is one I ran into in the past with my tau. I came home one day to find he had taken them all out of there cases and neatly arrayed them for battle against his mechs. Now credit where credits due he didn't break anything and he even did all the flight stands for drones and my devilfish. But keep your stuff looked up or high up if you want to be safe. Cause I also had the time were he decided to try and paint his mechs and upended a whole bottle of black primer to do it, I am still in trouble for that after almost a year.
Now I have been poking around for easy wargames for really young kids and even brick wars is a little complicated. But I do have a few ideas which I will being sharing in the future. Hope this helps any of you fathers or mothers out there.