Do solar systems have to evolve in a galaxy? Is it possible for a solar system like ours to exist and evolve apart from all other star systems and galaxies. Sort of like a stand alone solar system or rogue solar system for lack of a better name. Or is there some requirement that a solar system capable of managing and growing planets especially ones that will occur in the habitable zone originate in a galaxy?
Probably not. You'd need a could of gas dense enough to contract under its own gravity. In the space between galaxies, matter is spread too thin for a solar-system sized cloud to exist. A much larger cloud could be more diffuse and still collapse, but being much larger, it would collapse into a galaxy.

Even within a galaxy, stars seem to form when shock waves from nova or some other event initiates the gravitational collapse.