Is it realistic for me to dream for FAANG / Big Tech?

hey guys, ive been thinking about my future career a lot recently after seeing one of my friends get a good internship. i really want to get into one of these high prestige jobs but im wondering if it is even possible.

i have a 3.5 gpa, and i go to a state school (rutgers). i had a software qa intern in the past and a swe intern this spring. i also work as a mentor helping people code in our game making club

im a sophomore and i have been applying since ~november (sadly i didnt know about the process before) to not offer yet, but im gonna keep trying and land something this summer.

my goal is to grind leetcode, get a internship for the summer and apply like crazy in august-october. my dream is to hit the jackpot and get into these companies as a SWE intern and work in one when i graduate in the future.

but lately I feel lost like is it even worth it? my odds are so low, i'm wondering if my chances are even worth the grind.

any state school success stories out there?