Megafund PE out of Undergrad?

With the constantly accelerating PE recruitment, I was wondering about the possibility of breaking into PE straight out of undergrad. For context, I am a full-ride, low-income, international student at a target (Ivy) with a 4.1 (first year) and an athlete background (8+ years). I networked into getting a summer internship (unstructured) at a top buyside shop in southasia. It has been the greatest learning experience where they initially tested my technical skills and then directly put me on a live deal (obviously doing grunt dd & research under guidance). The firm is very lean and I have been getting facetime with the partners (one of them was a top BB's PE arm's Asia Head), sitting on client calls/meetings (taking notes) and overall soaking-in a lot. 

Can people give any suggestions, resources on how I could better position myself (or whether it's even possible) to break into megafund PE directly out of undergrad. (eg- BX, Apollo, Carlyle, KKR, Ares) 
I understand the importance of tenacity developed through 2 years of IB (has been mentioned across the board), but can I catch-up on the PE desk itself or do something beforehand to minimize the lag. This start of the summer has shown how intellectually stimulating PE can be (getting to hear about new, exciting prospective deals everyday and being in sync with the industry). As a person whose end goal is entrepreneurship, buyside seems to be where I can come closest to experiencing it before actually taking the plunge. Any thoughts would be great?