You're not required to have a loyalty program to have loyal customers.
The programs are just one way to organize different incentives you offer to customers. Instead of different deals or coupons, the customer would typically earn points that they can use to buy an incentive they want.
Customer loyalty goes deeper than how much someone claims an incentive.
Loyalty programs do make it easier to measure the symptoms of loyalty. Commonly you'll see customer balances and incentives redeemed. They aren't a measurement of loyalty itself but can act as a proxy.
You can also use other metrics as proxies for loyalty. Ultimately a loyalty program is causing customers to make repeat purchases and spend more with your store so any measurement around that can work just as well (or better).
In Repeat Customer Insights there are a number of metric options you can use. Repeat Purchase Rate and Repeat Sales Percentage growth are probably the best mid and long-term ones to watch.
Don't let the lack of a loyalty program hold you back from improving your customer loyalty. You can start working on customer loyalty today and grow your work into a program later on if you need it.
Measure which customers you're retaining and which you're losing
In order to keep your best customers, you need visibility into what's going on with them. Repeat Customer Insights will help you track down where you're losing customers and how to better target new ones.