No matter how big greek life is at your new school, it's not required to have a social life of any kind.
I'm hoping the reasons for your transfer to that school are focused more on academic or financial reasons than social life. If social life is a driving factor for that school, please reconsider. I agree that "feeling left out" would not help your mental health. So you need to find other social avenues.
Think of this, when you're done with school what kind of social activities do you envision participating in? How can you start those type of activities now? Intramural sports, clubs that focus on your interest, general friendliness towards others and inviting them to lunch/dinner/whatever.
Good luck with whatever you decide.
