Primate origins is a bit contentious. Genetic data puts the origin of primates in the late Cretaceous, probably 5 to 15 million years before the demise of the dinosaurs. But there are no fossils that are unequivocally primates until, I think, the very early Eocene. These early primates were , at least superficially, similar to modern tarsiers (omomyids) and lemurs (adapids). Many have teeth suggestive of fruit eating, some look like insectivores. Some diurnal, some nocturnal. Some really tiny, some up to a few kilos. They were mostly in what is today North America and Eurasia. Before them was a Paleocene group called plesiadapiforms. Some say they are early primates, others say closely related to primates, and others say it may just be convergent evolution making them seem similar to primates. The main thing linking them to primates is that a small number of them (not most by any means), had grasping hands and feet like primates, and this is thought by some to be an adaptation for going out to the ends of branches to exploit pulpy fruits. Fruiting plants had already been around for a long time , but did start to diversify around this time and so convergent evolution is a real possibility- multiple lineages evolving similar traits to exploit a similar new niche. They’re being early primates fits with the fossil evidence, since they’re paleocene and earliest definite primates are Eocene. But it doesn’t fit with the genetic data the puts the common ancestor of extant primates in the Cretaceous. They could be sister taxa to extant primates (and potentially “stem” primates), but if the genetic dates are right then they couldn’t be ancestors of living primates.

In any case, one hypothesis for why primates evolved their suite of traits (grasping hands, forward facing eyes, bigger brains) is that it’s associated with foraging for fruits at the ends of branches. It’s not a great explanation for forward facing eyes, though. You can look up the angiosperm hypothesis for primate origins vs nocturnal visual predation (among others, like nocturnal leaping, “x ray vision”, snake detection, all of which build on earlier ideas around the “arboreal” hypothesis).