I went to a UC. I've seen 2nd quarter 4th years get bids and graduate that year. I've seen international students only at school for their 4th year get bids and become well regarded active members.
It
can happen.
Based on your post response I'm guessing you're at CAL or UC Merced. I have zero experience with their recruitment other than knowing CAL is more traditional and UC Merced is fairly new.
Your best chance to get a bid is to go through recruitment.
If you haven't already, you need to figure out what connections you have to any of the chapters. Do you have friends or acquaintances in any of the chapters? Work on developing those relationships. If you aren't active in any organizations (on campus or off campus) see if there's anything you can get involved in now. It'll 1) pump up your resume, 2) give you something to talk about during recruitment events and 3) give you opportunities to meet more sorority women (potentially).