Working as an individual, you won't have the resources to build a website for a major corporation. No matter how good you are, you can only work so fast by yourself, and they don't want to wait years for you to deliver a website that takes 10,000 man-hours or more. Additionally, you are trying to climb a mile-high cliff with a stepstool. You can't jump straight from local indie freelancer to serving McDonalds.
If you want to some day be self-employed and working for the big boys, you'll need to be running your own team. You have two paths to choose from:
The "slow, always work for myself" path
- Assemble a local team
- Start from the bottom and work your way up. Approach local businesses and get contracts to build their websites. Every few jobs, go a little bigger and a little further. If you can show each potential client that you just did a project for a slightly smaller company, they'll feel more confident in you
- Start branding your team. Offer to shave a few percent off of a contract if you can stick your company logo at the bottom of each page, with a link to your website. Spread the word about your services and build a reputation
- Start landing large contracts with businesses that aren't local. Keep looking for bigger projects, but never tackle more than your team can handle - one major failure can undo all of the work you've done and leave your reputation in the gutter
- One day, you'll notice you no longer have to look for work, because big businesses are coming to you. Pick and choose who you work for
- Maybe, one day after many years of excellence, you'll get that email from McD's.
The "faster, temporarily work for others" path
- Send out job applications and get hired at a team that is at step 4 of the above list
- Work with that team until they hit step 5 of the first path, or get enough experience and then join another team that's already at step 5
- When ready, leave and form your own team. If you have enough experience and build a suitable team, you can skip straight to step 3 or 4 of the first path for your own team
You can get there faster by joining a team that already has the momentum, but either approach is going to take years. As I commented above, you don't go straight from the bottom to the top.