UX Newbie. What would be a good, quick way to test and prove my UX assumptions? [closed]

Last time I tried to redesign my college's class enrollment system. The problem is not everyone have access to that system, so it was hard for me to ask advice on internet. Also I didn't how to do research except interviewing my friends. The result is more based on my own judgement other than users.

I am trying to find an easy UX problem to practice. When I say easy I mean not redesign the entire site but improve a small function such as searching, filters. Here is my problem. Let's say I find an E-commerce website and I don't really like its search result page. I think it could be more comprehensive.

• How can I validate my assumptions?

First I was thinking maybe I could give out a survey asking if people prefer the current page or the page I am thinking about, but it is really hard to say which one is better before people actually tried both versions. Obviously I can't replace the existing page just for testing.

• If somehow I know that everyone have trouble with this page, and I come out with a new design. How could I know that my design is better without actually implement it on the page?

I am just looking for a random site to practice so I can't get help from website's actual owner. How could I test my result and prove that mine is better