Not legally. Practically, almost always.
The direct answer
Nothing requires a first-time author to have a website — you can publish a book on KDP with nothing but a social media profile. But a website is the one place online you actually control, which a rented social profile or a retailer's product page never is. For most authors, that difference becomes noticeable fast.
When it matters less
If you're publishing one book purely as a personal project with no plans to build a readership, promote future work, or be reachable by readers or media, a website may genuinely be more than you need. It's not required — it's a practical tool for authors who want an online presence they control rather than one they're renting.
What a first website actually needs
It doesn't need to be large. See what pages an author website should have for the short list that covers most first-time authors, and how much an author website costs for what affects the price.