When I first started out, by far and away the most effective method was word of mouth via people I'd worked with as an employee. As soon as it became known that I was looking to take on freelance and consulting work, the phone started ringing. More often than not it was someone who personally knew my work, or who knew someone that did.
I've had some success at trade shows. You could try either dedicated electronics and manufacturing shows, or alternatively, shows dedicated to product areas you'd like to work on. They can be great opportunities to meet with senior people who wouldn't otherwise take your phone call. Take a pile of business cards, and if you have something relevant you can show off which will fit in a backpack, so much the better. You might not get any work straight away, but people will remember the guy with the <insert project here> that they met at <event>.
It's worth setting up a reasonably professional looking web site first. You may not actually get any enquiries through it directly, because actually getting your site to appear in search results is a whole ball game even on its own. However, people who find out about you through other means will check it out, and it adds a good deal of credibility. A business card and a web site are much more effective together than either is on its own.
For what it's worth, I'd seriously question whether "most" people expecting to make a good living as freelance engineers start with Upwork, or any other similar sites. I have no interest in competing with overseas engineers in a race to the bottom for both price and quality, and never considered them my competition. My customers need relevant expertise, experience, and on-site service - and that means we're serving entirely different markets.