being international definitely doesn't help and it's also not something you can really change.
So they claim that they are looking for people with the capacity to do really great research so having good letters of recommendations from a top lab, publications, extensive research etc really helps. However, I learned this year that that alone will not get you into the top programs. Unfortunately it seems like a lot of programs do have GPA cutoffs and with a subpar GRE such as myself that's not great.
I think that the applicant most likely to get in already has top grades - if you look at the profiles on people at gradschool cafe I notice that almost everyone getting interviews has a 3.7-3.8 and great GREs. I thought that this wouldn't necessarily be the case, but it seems like it is. It's probably this and then a connection to a lab at the institution