A REST API typically does the mundane CRUD operations on data so you would definitely need a database.

More importantly, who is the customer? Companies w/o developers wouldn't probably be building an API, they would be looking at full services they can just pay for with a CC. Companies with developers can scaffold a REST API with some web development frameworks out of the box.

Who is the customer and what value does this SaaS bring?

How will you handle API authentication, rate-limits, scaling, analytics, etc.?