Can I get research experience at another University?

I want to gain research experience because I want to be accepted for a PhD program in a few years and be a professor one day.

Unfortunately, my small, unknown University (Interntaional tuition, can’t afford any better) has almost no research at all…

Now I thought about writing to the University of Victoria near me next year and asking them if I can volunteer as a research assistant over the summer or something. Do I have to be a student at a University to gain research experience? Is it possible to get research experience at a University that I’m not attending, or is it very unusual? I study in Canada btw

Thank you

you can certainly apply for Summer research programs in your area of study at different colleges.
Going to them will certainly be considered in your PhD applications.
Research is research.