Alabama Kid Cracks Big Tech?

Hi Blind, I am getting ready to apply to FAANGMULA etc. tech companies, maybe even Albertsons if I'm feeling brave. I have been doing some leetcode lately, and am I able to complete most mediums within 20 minutes. Some hards I complete relatively quickly, but others are just too hard. Generally, in contests I complete 3-4/4 problems and place in the top 4-8%.

My worry is that I may not get many interview opportunities. Before I graduated university two years ago, I grinded leetcode + resume. I got 0 resume screen passes from top tier companies even though I had my resume professionally reviewed and applied as much as possible. I had one internship and some side projects. (I got plenty of interest locally from lower paying jobs and less famous companies.)

Could going to a low ranking state university for my CS degree and living in Alabama contribute to this? If so, how do I mitigate the damage and signal to top companies that I could be a solid candidate? I know that putting leetcode stats or test scores on the resume is a no-no. I won some math competitions in elementary and middle school, but I'm sure that would look even more tacky.

I work as a mostly backend developer for a local startup that uses .NET + Azure Cloud. I will likely get a raise soon as my boss has good things to say about me, but I don't know how much. My previous job was Python based. Wife prefers to continue living here, so looking for remote work.

Additional Questions:
Is there any point in waiting until 2 yoe to apply? I've heard it is when recruiters start reaching out more, and it might look bad to jump around so soon?
If Amazon is the only big tech company to give me an interview do I take the job or would it mark me negatively in the future?
Could open source contributions give me an edge?
I've been working on a Golang + React app, would polishing and featuring that get me some phone screens?
Maybe referrals are what I need? Best way to get them if your friends don't work for Big N?

Thanks <3

TC: 70k
YOE: 1yr 8mo