My daughter is a 2nd year CS major at UA. She got a co-op (at Nucor) offer last semester (so, 3rd semester on campus . . .she came in with 41 AP credits, so she was already technically a Junior) . . .
Students mostly participate in the co-op interviews 2nd semester Freshman year, 1st semester Sophomore year (when my daughter did it), and 2nd semester Sophomore year (is kinda’ late). So, go by that, and start try-ing in the co-op program the second semester you are on campus.
Even though you come in with a bunch of credits (as did my daughter), not much of those are relevant to CS, so you won’t know much that is useful to a co-op company until you have a few CS classes under your belt.
It’s tough to graduate in 6 semesters on campus in CS, but possible … Study the flowchart, consider the pre-reqs, and schedule carefully. (You’ve got 8 semesters of “free” tuition on the Presidential . . . consider doing a MS if you have time . . . My dd is a National Merit Scholar, so she’s got 5 years . . . and is planning on doing 2 majors and a MS in those 5 years).
It seems like in the fall, there were a total of 6 companies doing co-op interviews for CS majors. My dd wasn’t interested in a couple of them, and got interviews with the 4 she was interested in. You only need 1 offer, and you can only interview with up to 4 companies (maybe one or two more if you get on wait lists).
I don’t know anything about the impact of being an international student. 