Need career advice

Hi, some context first - I'm a student from one of the BITS campuses and currently in my last year, interning at a Fintech based out of SF, with an office in Bengaluru. It's a good company, and work is nice. They're offering me around 15 LPA in-hand (some esops, no variable pay). While it is a good offer and I like being here, I wanted to try out my luck for some bigger companies/established startups - for higher pay, that I can negotiate here or switch to the company depending on work culture. I'm looking for something that maybe offers around 20+ LPA, but I'm not able to get any opportunities. I tried cold messaging on LinkedIn but that didn't work either. I am planning on trying for placements next semester, but since my CGPA is a bit on the lower end, I don't want to be too optimistic on my chances there. Plus, most companies that come to BITS in the second semester pay a similar amount. Wanted to know how I can proceed? A lot of startups are not hiring SDE-1 at all, and some require 1 year of experience. Is it possible I'm looking for something that isn't possible in the current market?