You got the first part 50% correct. You got the second part 100% correct.
Companies don’t prefer well-known companies to build their website because of their name cachet. They prefer people who can do the job well, and have a track record/proof of it.
The fCC portfolio may be good material to get into an interview for a web dev position, but it’s not good material to attract a client, you working as a freelancer.
You need to be showing some real website designs in your portfolio to attract clients. Not some pomodoro, tribute page, or weather app. (As I said, these projects are good for getting an interview, but not for getting your own clients). Then you may ask how can I show a website design if I don’t have clients? You make hypothetical clients! – here’s what I would design for a law firm, a bakery, a small business, a car repair shop, a realtor website, etc etc. Showcase your design chops.
Another option is to do websites for non-profits in your area. Offer your services for free. Some business don’t have a website? Offer to design their site for free, in exchange for some good testimonials for your work. They only pay hosting. Then include their site, and their testimonial in your project portfolio. (Actually, you can make a little money by charging them web hosting + management + backups… host them on your own reseller account, and charge them $25/month. It doesn’t cost you anything, and you’ll make $300/yr for each client).
The board members in non-profits usually have some other job, or know people who know people. Build contacts! If they like the work you did, they may refer you to their own company, or another company.
When you finally get a paying client, ex: working with small businesses, they’re scared seeing PER HOUR rates. Because they don’t know what they’re getting, and what eventually they’ll pay in the end. Bid on their projects on a fixed rate… $xxxx amount to finish everything we agreed upon in the contract. Since you’re just starting out, your estimate may be out of whack. But who cares! You’re just starting out… think of it as real-life education and experience. If you have to, work at a loss just to build up a portfolio and experience from the start.
It’s true that in Israel there is a lot of work, but in freelancing many people prefer paying twice the price for a big company to do the project.
You need to get this BS thinking out of the way. Prove first you can do the work, then you can charge as much (or even more) as these big companies do as a single developer.
You said:
I implement those skills while building websites for my clients, whether it is plain html, css and javascript or Full Stack web apps using ReactJS/React Native with Nodejs servers.
Prove it. Show some real, practical websites that potential clients will get excited about.
Also, most clients don’t really care what you used behind the scenes. Couldn’t care less if you used ES6 or Node or whatever. But they want a beautiful working website, functional, that will attract customers, paying customers, that will help grow their business and make them more money. Show a track record that you can deliver these goals, and you can charge as much as you want.