Well there are 20 top 20 schools if you use one pub or prob 30-50 depending on how many sources you use.
You are unlikely for a U.S. News top 20. You are highly unlikely for Cornell and Columbia, based on class rank alone.
You can certainly try.
But there are MANY great schools out there and going to a school that a magazine (not the real world) has decided is tops is not a guarantee of success.
Your strategy is fine but you need a balanced list of schools that fit your personality. I assure you all top 20s don’t.
If you will only consider top 20, you also need to prepare for a gap year and or community college.
I hope you get what you want but it’s not likely.
It’s now four years (class of ‘21) and I think it’s more competitive now but my daughter’s Valedictorian with 4.0 with 10 or 12 APs who applied to 16 of the top 20 got into exactly zero. Got into NYU full pay attends UTK (our in state).
You need a real plan. I’d start with figuring out what you want in a school and go from there. Columbia isn’t Dartmouth.
You will be somewhere four years, day after day and you want to be happy.