Yes,I get your point.My product is an AI Rap generator, website: rapgenerator.net, which can generate Rap lyrics through AI, and can also generate Rap music through lyrics. My goal is to enable every Rap enthusiast to easily create their own music without needing to learn very specialized knowledge.
Ideally they tell their friends. But it may not be that kind of product.
So don't be shy to get some testimonials from them. You can be pretty blunt;
"As you know xxx is a new product and I'm trying to spread the word. I'm looking for customer quotes for my web site, so if you have anything nice yo say I can publish there, please let me know."
Exactly. You go to the customer, they don't come to you.
It can take time, and consistency, but persistence in a good way) builds up trust.
Equally it acts as a view into you. Are uou generally helpful when interacting, or just pushing you product. I became an "industry expert" - helping whoever and however I can. Regardless of whether it pushed my product or not. Equally where I had a product that solved an issue I didn't hesitate to mention that as a solution.