You have to RESEARCH that for each university individually - and once you learn that there is some application process, then follow whatever deadlines, requirements, submission of essays/material…, which can further vary for various different scholarships they might offer!
Some will throw out some merit scholarships to entice interesting students, without even asking.
“Not qualifying” usually applies to financial aid, because your income/assets might exceed thresholds.
In contrast, merit scholarships (typically) are open to all income levels because they are based on (drumrolls…) merit! The most elite/selective schools don’t offer merit scholarships at all, because all their applicants are equally highly meritorious.