It's possible defiently. But it depends mostly on your creativity.
For me, because of my high creativity its not still not easy to come up with something completly new (of course) but i can come up with a couple unique ideas
to how you can create a new genre.
It may seem impossible at first. But when you come up with an idea try fantisizing a world based on that idea, i think the rest of the ideas might just start flowing in
Thats how a game is shaped (At least thats how i come up with my games)
to come up with an idea for a new genre: Try picking one idea, expand, then complex it and draw a system that shows how the idea works. Then start adding random stuff combine expiriment, just try something new and the idea might appear inside your head.
then the rest... i have no idea....
But if you can't make a new genre, try picking a genre that already exists, look for flaws that the games, based on that genre has and try creating an idea around that.
(This is my own way of creating games idk about you guys but this is all i can say.....)