Your son sounds exactly like mine was, but he was only 18 months old when he started crawling out of & literally jumping down from his crib. We transitioned the crib into a toddler bed more for safety than anything else, but he was the same as yours. We would put him to bed & no sooner did we close the door did it open right back up again - a dozen or so times every single night for what seemed like forever, though I think it was only for a few days. What I finally started doing was sitting in his room in the dark by his door after putting him to bed & letting him know I was there & not to get out of bed. I guess just knowing I was there prompted him to stay in bed, but it didn't always work. I used to try to quietly "sneak" out when I thought he was almost asleep, but sometimes he would hear me & start to get out of bed, so I'd have to tell him I was still there & not get out of bed. I think I had to do this for several weeks before he finally would stop getting out of his bed, so it definately took a ton of consistency & patience as well b/c of course as I'm sure it is for a lot of parents, we have "our" time after the kids go to bed.
Even after he stopped getting out of bed after we would put him to bed, he still had issues getting out of bed in the middle of the night & coming into our room & we just "dealt" with it by walking him straight back to his bed & telling him not to get out of bed & that he is supposed to sleep in his own bed. Well, low & behold when he got too big for his toddler bed at almost 3 yrs old (we had used the crib mattress still b/c the crib had transitioned to a toddler bed), we got him a twin bed with a nice comfy mattress & he stopped getting out of bed in the middle of the night. We realized then that it might have been the crib mattress that was uncomfortable for him, but we were so relieved to finally start getting some uninterrupted sleep! Luckily for us, his twin sister has always gone to bed w/o issues & didn't get up in the middle of the night like him. Anyway, just be consistent with him in putting him back to bed & make sure he has a comfortable mattress! Good luck!