I'm curious as I've been recently playing a lot of medieval games like Mount and Blade, and of course it being a game it's not going to be the epitome of realism (but I do think M&B is pretty close on medieval gender roles), however I would like to know if it would be possible in medieval times for peasants, or merchants, or low-born workers to ascend the hierarchy and become knights, counts, barons, or even kings. I know it could have happened in Rome (like with Justinian, and to a lesser extent Caesar), although it was harder in the Republic, but I'm curious about Western Europe in particular.
By the start of the High Middle Ages it was impossible. A candidate for a title, say, the younger son of a younger son, still had to be able to prove all four of his grandparents were noble - no commoner grannies.
The base-born lacked the opportunity to rise into a warrior nobility early on, except through military prowess, starting with getting a berth as a man-at-arms. If they were good and lucky they might make knight, and marry a nobleman's daughter. Then their grandchild might be eligible for further advancement.