What if humanity discovered the Prothean ruins and Mass Relays much earlier?

Interesting idea, hard ot say. I suspect in the Me universe they were more world government focused by the time they got to mars. But if we found it pre-cold war ending who knows. Those were crazy times. If russia found it they likely would not have collapsed,and a world war would have been likely. If the USA found it a bit less likely for a world war, Russia would have still collapsed but American imperialism would have been even larger. Tech leaps like that don;t end pretty imo unless everyone is mostly getting along.

If humanity discovers the prothean ruins during our time, I would guess the plans for the crucible would have been found long before Shepard is born. Since the plans are not prothean specific, according to Hackett, it wouldn't be hard to build it. Humanity would likely wonder why there are plans for building something so big. What purpose does the thing serve? They likely won't know until they settle on Eden Prime and then on Feros. On Feros would the plant give a human the cipher to be able to activate the artifact on Thessia, if the asari allow humans to check it out? No matter what, there's a chance the crucible could have been used long before the reapers entered the galaxy.

If 20th and 21th century humans had FTL drives would be like giving cavemen nuclear weapons results would be disastrous. We're not ready for that kind of technology and we would lose the First Contact War against the turians or any other race in the Mass Effect (or any other sci-fi action series/franchise) because they would kick our asses so hard and so fast before we knew what hit us.

If present day humans discovered the Prothean ruins and managed to actually reverse engineer the technology it presented into something remotely affordable and usable, its effects now would probably not be much different from the effects it would have on humanity discovering it in 2119. Leaping to FTL today would more likely just result in a lot of slingshotting across the solar system for a good number of years before actually going a whole lot further. It’s even less likely that anything that actually leaves the solar system itself would even be armed. Even if they violated some galactic law and got policed by the turians, it’s doubtful the turians would really start a war over some unarmed exploratory vessel. Aside from that, the asari and the rest of the council would not permit this little police action to escalate anyway. 

Nationalistic rivalry might make human expansion even more rapid than it was in the original timeline, assuming that the technology became widely available. Who gets involved depends on how expensive you figure such a project would be.

I guarantee whatever country found the ruins would use it to gain absolute superiority over the planet.