Nope, actually do everything to get the first few to pay. Once you do that, you can at least be certain that there are people willing to pay for your service/product. You can focus on growing your customer base after your paying customers give you great feedback.

Seems like a bold move. I feel like if I tried doing that, I'd get requests for refunds and a lot of bad press. But I guess your point is that at least I'd have to learn why, and then fix that for my next trial.

Why do you think it is a bold move? Since you have a handful of customers in the beginning, things can never get out of control. Even if your customers don't like the service/product, you can still do something about it - you cannot do it if there are hundreds.