My first thought was why don't you start out in Canada and after you have gained some experience working there you can figure out how to move to the US. It will be easier to figure out then.
another option: Study in Canada and get an internship at NASA.
I also want to suggest that you contact NASA and ask some questions. Do they sponsor visas? What if you graduate at the top of your class? Do they make any exceptions? They will probably say no. You're a stranger. But if you get your foot through the door first as an intern, you might find another answer or learn of another option.
a few other things to think about: 1) there is a program for international university students called Optional Practical Training (OPT) and another called CPT. These programs allow you to work in a degree-related job for one year after you finish your studies. I believe it is offered at many universities. It is possible to find an employer who will sponsor your visa. You just have to look hard. I would even start looking before your study program ends. ( of course this will be easier to do if you attend university in california).
2) the US is one of a few countries that grants citizenship almost immediately, if you join a branch of the armed forces. The only stipulation I know of is you just have to pass your basic training and of course, finish your service. Your citizenship is granted after you pass basic training. You don't have to go into combat if you don't want to. My friend joined the Air Force and worked in administration. She just finished her service not long ago and has returned to civilian status.
Some things are not as set in stone as you might think.