I'd go beyond possible into probable. As said, Mass Effect makes a point of an extremely small portion of the galaxy having been officially mapped out/explored, partially due to the post-Rachni war sanctions that had relay activation become a rarity. If you look at the timeline there were huge gaps of Earth years where species existed or co-existed before running into another.
Asari owned the Citadel for 60 years before they met the Salarians, and across an additional 500 years they met various species before bumping into the Rachni. It took nearly another hundred years before the Krogan were uplifted. Then about another 500 years before anybody even knew the Turians existed. It took 1500 years before the Drell and Yahg entered the scene, then another 30 or so before Humanity came in contact with the Turians. In actuality, the Asari/Salarian/Turian trio ruling existed for about 1500 years before Humanity was even known as a species. And not consider that the time between Humanity's first contact with the Turians, and finally the end of Mass Effect 3's Reaper war, was only about 40 years. It's an exceptionally (and questionably written, though nonetheless canon) window of co-existence.
That should put into perspective the passing time frames and the overwhelming scope of the galaxy, and how easily a species could evolve into a space faring, discover "Prothean" technology, open up a few relays, colonise a few worlds, all without ever coming in contact with Asari, Salarian, Turian, Human, and everyone else. Every species has been in that position. The difference being a new species might make first contact after the Reaper war has ended.
And while it's easy to assume that the Reapers would have found a new space faring species, that's not entirely accurate given how disrupted the harvesting cycle was. Originally the Reapers would bust into the galaxy via the Citadel mega relay, then use the Citadel's collated data as a census on all active, contacted space faring species, their home worlds, colonised worlds, and use such info to strategise the harvest. This time that never happened, at least not until the very end. The bulk of the Reaper forces were focused on the known species and their home worlds as it was now more than a harvest: it was war. Scouts were sent out to smaller threats. While it's entirely possible such scouts would run into a new species, it's also entirely possible they would not.
Imagine: You've got a patch of galaxy that has never been accessed by any known species. It's never been mapped or explored. Nobody has traversed its space, and no Council space relay has connected to it. The Reapers attack, and they assume as much as everybody else: there's nobody of value there, certainly none of the threats, so there's not much point throwing resources at what could very well be a big pocket of empty nothingness.
Except there isn't nothing. There's a space faring species. They've found technology. They've unlocked relays. They've colonised worlds. They're yet to make contact with any other species. And they're about to do just that.