A short answer to this is NO. While you can reduce your costs by building a website yourself, you will have to invest a lot of your time. On top of that, you will have to pay for hosting, domain name and other services.
You can try to use a free website builder like WIX, but even their free version has a lot of disadvantages like ads on your site, you can't use a custom domain, etc.
A website like that will not look professional at all and will make your potential clients suspicious.
That's why I don't think that you can build a real website for FREE.