Yes, it is possible to build a website for free, but if you need a professional website, the answer would be a no. You can find free website builders, but when you look closer, you still need a budget to get things up and running because in free versions:
You can’t have your own domain.
Website builders don’t allow full control over your website.
You’ll need to pay to access themes, templates, and add-ons.
Your website will be crammed with ads.