How to not get "filtered out" during graduate admissions in top programs? There are a lot of questions about admissions on this forum, including many which discuss the importance of the GRE. However, my question is a little more specific than most of them.

In short, what does it take to not get "filtered out" of graduate schools admissions, particularly in competitive engineering/STEM programs?

I have read some answers on this forum that mention that candidate profiles are divided into MAYBE/PROBABLY NOT/NOT groups, where applicants who belong on PROBABLY NOT/NOT groups may not have their applications read by faculty--which makes sense, given the hundreds of qualified candidates they can choose from. (See this and this). This practice is consistent with what I've heard from other professors. However, what does it take to not automatically fall into those categories?

JeffE, for instance, mentions that, in his school, candidates are/were filtered by GRE and GPA. How does this process work? Are GRE/GPA scores the only filters or are other qualifications taken into consideration during the initial triage (i.e., publications)?

For instance, I received unimpressive GRE scores (~90% Q / ~70% V / ~10% AWA, ran off-topic). Moreover, while I ranked first in my graduating class, I am an international applicant from a (top) Latin American school and the committee may not be able to interpret my GPA. While I could take the GRE again and score better, that would consume time, energy and money (getting to the nearest test center requires 10+ hours of travel as well as sleeping over), all of which could be better spent in other parts of my application. Nonetheless, I believe I have an otherwise very strong application, having various first author publications in top journals and conferences, very strong LORs, 5+ years of research experience, and regularly serving as a reviewer for a top journal in my field.

However, my concern is to be rejected in the initial triage, given that I have no idea about what would get me past it.
The easiest way is to get buy-in beforehand. Find a specific PI you'd like to work with and contact them, best if by phone, preceded by email. Express your interest and how groundbreaking you find their research, and how you can uniquely contribute to their research program. Usually this gets you off the pile and onto someone's desk. The school may have cutoffs for standardized test scores, but even that can be mitigated if you capture a specific persons' interest. The point is, make a personal appeal to an individual.