With a standard Squarespace account, no. Every site starts from one of Squarespace's starter templates. The exception is Blueprint AI, which builds your starting site from your answers instead of a template you pick.
Empty a starter template: Pick any of Squarespace's starter templates and delete every section. You're left with empty pages to build on with Squarespace's sections, blocks, fonts, colours, and design settings.
Use Blueprint AI: Squarespace's Blueprint AI builder asks about your goals, brand, and content, then generates a multi-page site you can preview and edit before publishing.
Work with a Circle partner: Squarespace Circle partners have access to a blank template, which designers can use as the base for custom-designed websites.
Whichever route you take, Squarespace is template-based at its core, so you're working inside its design system rather than coding every element. Complete customization with CSS and Javascript are available on Core and above for smaller changes. A fully custom-built site is generally a better fit for WordPress or a custom development platform.
Starting from scratch gives you the freedom to design your website from the ground up, but it takes the most time, because every layout decision is yours. Squarespace's starter templates usually need fleshing out too, with more pages and copy written for your business. That's where August Cura Studio templates come in. Each is made for one type of business, with the pages it usually needs already laid out, so your time goes into your own words and photos.