Should I wait until I have a stronger profile to connect with schools?

It depends on you. You can reach out about questions for their programs, what they look for, etc, etc. Since you are on here, I assume you are building your college list... So as you are looking, reach out! Tell them what you are interested in, why, and what makes you attracted to the place. When you schedule an interview (3-4 months later, but again you decide when you feel your profile is strong enough to impress at an interview), you can expand upon what you are doing and more.