Uncharted 3 and 4 certainly do not provide an "origin". They tell us chunks of Drake's background - how he met Sully, how he found out about his family history... But they don't show Drake "becoming who he is today" - assuming that by "origin" this is what they mean.
E.g. Naughty Dog never felt it necessary to do a Tomb Raider 2013. We always knew Croft's background - we never knew her "origin", when she becomes the legendary treasure hunter.
Naughty Dog know that doing a proper "origin" of the character (ala Tomb Raider 2013) would not work at all in a game. So they never touch it. E.g. Drake's first kill, his first big thefts, his escalating career...
We never see that transition in the games - we never see that origin.
A movie, frankly, will be way better at covering that sort of ground.