I started on Upwork with a very low rate (~$20/h) and applied to as many jobs as the platform allowed me to, with a custom cover letter for every single one. It was time intensive, but without any reviews it's your only way to stand out.
After I got my first project, I made sure that my client was blown away by everything: communication, turnaround time, code quality, etc. When I was sure the client was happy with the result, I asked him if he could leave me a review describing the process of working with me. By asking, you're letting him know that his review matters, and he'll probably put some extra effort instead of just writing something for the sake of it.
I kept (slowly) increasing my rate and continued sending custom proposals for clients. This is your advantage over all the low bids you can be sure they're getting.
After a few projects under my belt, I've built my personal portfolio, making sure Upwork reviews were there, along with a small description of the projects I completed. I've published my portfolio around in a few relevant websites and this has brought me client work directly to me a bunch of times.
After a while, you'll notice you're getting more proposals than you can handle, mostly uninteresting and low pay. That's when I've set my Upwork rate to something high enough that clients that weren't serious just wouldn't contact me.
I was 20 when I started doing this. I'm 23 now, with my MSc almost complete (just delivered my thesis this week) and a remote job working full-time at a startup with a great salary.
This is not a fool-proof plan, I may have gotten lucky here and there, but it is absolutely viable to do this without a resume. I've never had a resume to this day.