How to get an opportunity to interview at big tech?

I recommend checking out these other resources:

• "I want to land a job in a big tech as a SWE - How to do it?"
• How To Get FAANG Interviews

Keep in mind that this economy is extremely bad, especially for Big Tech jobs. Keep expectations realistic and really focus on how you can stand out (the resources above cover some tactics to do this).

For improving your resume, I strongly recommend our resume optimization masterclass: [Masterclass] How To Write A Stellar Tech Resume That Gets You More Job Opportunities

... though my resume is not getting shortlisted, so I rarely try applying and keep studying.

Continuous studying without clear action attached isn't the best use of your time IMHO. I think you should apply right now (you never know until you try!) and see what you can get. Check out these other discussions which cover this balance more in-depth:

• "How do I balance my time between studying DSA and fleshing out my portfolio?"
• "Fighting Perfectionism as a Software Engineer (and getting important stuff done)."

There are 2 distinct phases for getting a big tech job:

• Phase 1: get interviews
• Phase 2: pass the interview

Until you've passed phase 1, I would not spend much time preparing for DSA interviews. Just focus on improving your profile (building projects, networking) so that you get an interview.