An early adopter (sometimes misspelled as early adapter or early adaptor) or lighthouse customer is an early customer of a given company, product, or technology. The term originates from Everett M. Rogers' Diffusion of Innovations (1962) https://en.wikipedia.org/wiki/Early_adopter
While I've often seen it used most often in reference to the Technology field, this term can be used for the first people to start using any new product, technology, or service. While it might seem a bit pretentious to say that a barber shop, for example, has early adopters, the role of an early adopter (feedback, reviews, influencing others to use the product or service) applies just as much for a small business as for a new startup or technology.
On the other hand, if you want a term that simply describes a business' first customers without implying that they might "adopt" the use of that business, or that they're more "adventurous", "influential", or different in any way other than the fact that they happened to come by first, then the most common term seems to be just: First Customers
See these articles:
How Uber, Airbnb, and Etsy Attracted Their First 1,000 Customers,
How To Close (And Keep) Your First Customers,
Landing Your First Customers, etc.