I think finding a friend group is crucial in getting you through college. If you have friends at the big school already I think it might be a good choice to transfer especially since that school offers you more options on what to study. Go ahead and put in the transfer app. It’s not committing you to anything except the cost of the application. Filling out the transfer application just gives you choices.
Go visit your friends at the big school for a weekend — maybe go to a football game or other event See what it’s like there for a weekend. Even better, if you have any Fall Break days when the big school still has classes consider visiting then and sitting in on a few classes and see what it’s like being in bigger classes
Continue to try to get involved at your current school too. You may finally click with someone there and might find a new interest for your major.
But definitely fill out the transfer app. Filling out the app is not a decision to transfer. It just gives you choices.