Getting into Houston IB (SA) as a spring transfer

I am a 2nd year student at a non-target (ranked in the 30s) transferring to a target (Rice) next semester (spring 2021) and was wondering how I would go about getting an IB summer internship for junior year.

I have a high GPA at my current school (3.95+). Would banks care that this GPA is from my non-target if I am already at a target when recruitment starts?

Will my peers have an advantage over me because they have been involved in business ECs/clubs at a target or have previous internships while I don't?

How difficult would it be for me to get a SA offer at a BB (MS, GS) and how much work would I have to put in cold-calling or networking? Would it be possible to get a SA internship in my sophomore year and would this help me secure a BB/MM SA internship (Jefferies, EVR, MS, Citi) for my junior year? 

Lastly, how should I start preparing for SA internship given my situation? Do you think I have a chance for BB IBSA?