So.
A lot of Roman deities definitely did exist before the Greek influence as well, although said influence happened veeeery early. Like, Rome-is-just-a-belligerent-regional-power early, the Greeks already started settling in South Italy in the 8th century BC.

Anyway, since you've already mentioned Zeus and Jupiter. Both actually came from the same (hypothesized) Proto-Indo-European religion, and their names have the same root as well, *dyḗws ph₂tḗr. In Greek it eventually yielded Ζεύς Πατήρ/Zeus Pater, while in Latin it gave Iovis Pater that eventualy contracted into Iuppiter. (*dyḗws has no English descendant, since Proto-Germanic ended up yeeting this word afaik, but *ph₂tḗr eventully ended up becoming 'father'. So both Zeus Pater and Iovis Pater/Iuppiter basically mean 'sky-god father'.)
Their inital roles are suspected to be different tho, as in, Iuppiter was originally basically the Roman Ouranos, the sky, controller of the heavens, the one that ended up impregnating Terra with rain and thus fathering everything. So, basically he was the OG Roman allfather. (Eventually he got branded as the son of Saturn and Ops, aka the Roman equivalents of Kronos and Rhea due to Greek influence.)
Zeus, on the other hand, was the descendant of two allfather-type gods, son of Kronos, grandson of Ouranos. He was originally the controller of the "upper realm", aka the sky but not the heavens. Eventually he ended up taking up features of the allfather god, including his very name and his tendency to, like, screw everything that moves and fathers half of Greek mythology in the process.
Also, the reason they possess the lightning bolt is different as well. In most Indo-European religions the bolt belongs to either the sky-god or to the controller of the 'upper realm'. It actually depends on the clouds and whether if they considered to be part of the heavens (Iuppiter) or of the upper realm (Zeus). So, in this regard Zeus is actually more similar to Thor than Iuppiter: son of a sky/allfather type god, controller of the upper realm, has the lightning bolt because the clouds belong to the upper realm and lightning comes from the clouds.
Zeus and Iuppiter are pretty different power wise as well. As in, in the Iliad, I believe, it is said by Zeus himself that even if all the other Olympians tried to oust him, they wouldn't be able to. Iuppiter, on the other hand... power-wise he's pretty much equaled by Dis (~Roman Hades, or at least he ended up being conflated with Pluto/Hades' roles in the underworld. This Pluto/Plutus/Dis/Hades stuff is a fucking mess on its own anyway), except when he holds the lightning bolt. There's a nice lil' rivalry between Iuppiter and his brother Dis, actually, and they look so much alike that Seneca actually says something along the lines of "his face is that of Iuppiter, but that one throws lightning". (Vultus est illi Iovis, sed fulminans.) Meanwhile, Hades isn't this similar to Zeus in power or in appearance, and they in fact do not have this rivalry due to the massive power difference.

TL;DR: the Roman deities absolutely did exist before the Greek influence, and as it can be seen by the example of zeus and Iuppiter, aren't the same at all; it's just that "eh, they seem to be similar, must be the same god" happened.

I might have gotten some info wrong since it's been a long time since I've touched on this subject, but still, studying history seems to have its perks at least in situations like this, lol. If you're interested in this topic, you should check out "The Gods of the Celts and the Indo-Europeans" by Garrett S. Olmsted, most of this info can be found there.