App ready to go, but how do I get my first customer? Or should I give up?

I have created an app, teensybit (teensybit.com) to manage small home daycares. My mom has a small home daycare, but she hasn't proven to be a great first customer, even though she has helped test things a bit.

What are some ideas to get my first few real customers? I'm game to spend a bit of money, maybe up to $100, but I want some confidence what I try will have as high of success rate as reasonable.

I have reached out to a facebook group manager that said they could run an ad for me, but that would start at $250, so I'm not quite ready for that yet.

I've also directly reached out via email to some local daycares, but haven't had success with that.

I'm not sure when to take these failures as my app/idea simply won't work, at least as advertised.

I'm open to all ideas and advice to get some customers

Thanks!