When I came from Nepal to do MS i didn't had any support either.I carried the first semester fee and come and paid here.After that I started looking for assistantships and got it and they reimbursed my payment.There are three kinds of assistantships international students can get like I mentioned TA RA and GA.

GA is someone who will work outside the departments i mean if you are joining Chemistry department for your grad program  but can work in Physics department as GA.

Teaching Assistant(TA) is the one who will assist the prof in teaching students like preparing slides for lecture,grading students exams it can be lower lever than your program.I think they usually give you on your own department.

RA is also is same department under your professor and you will be helping prof to do research or some administrative work as per requirement.

In all these cases TA,RA,GA you will get instate tuition(one third of what international student should pay) and also they will pay you for the hours you work which is in most cases sufficient to cover all expenses.

GRE score is for getting visa so doesn't count that much in getting job since I had score like yours and still got one.I suggest you not to join Phd without funding but I think you can come by paying  and come and try here and you will always have other options to search.Hope that helps.Let me know if you need more info.