Why do I keep getting rejected despite referrals? Am I just not eligible?

I’ve been trying to get into companies like Big4 firms and Deloitte. I reached out for referrals, tailored my resume, prepared well, and did everything I could think of.
For context, I worked at Reliance for around 2.5 years and recently moved to FirstCry. I’m trying to transition into better Product/Project Management roles, but I keep getting rejected before I even get an interview.
Now I’m wondering:
Is FirstCry not considered a strong enough company?
Does moving from Reliance to FirstCry somehow make my profile less attractive?
Or am I simply not competitive enough for these roles?
I’m not looking for validation—I genuinely want to understand what recruiters might be seeing that I’m missing.
Has anyone here been in a similar situation? If you recruit or have hired for these roles, I’d really appreciate an honest perspective on what could be holding my profile back.