Yes. It is possible to luck into a solution if you don’t know a method. But it’s pretty rare, and if you don’t get lucky, the best most people will ever do is to have a mostly solved cube.

To go further requires you to use predefined sequences of moves that at first appear to mess up the parts that were already solved, or to systematically work out those sequences yourself, which would involve some serious effort with extra cubes or with writing down sequences on paper or something similar.

It’s counterintuitive, but at a certain point, if the cube is mostly solved, but the last bits are wrong, the only way a normal person could solve it without these sequences is to completely mix up the cube again and start over, hoping to get luckier the next time.

I don’t know the odds of getting lucky like I’ve said. I used to practice cubing just to pass time, and I’ve probably completed hundreds of cubes, and only once did I luck into a solved cube without using those sequences. And I assume I was lucky even with that.