For every Facebook you quote me, I'll show you 10,000 others that didn't succeed and instead wasted time and effort when they could have done some customer research exactly like this.
Why would you invest that much? If your minimum viable product takes months and thousands of dollars you're doing it wrong.
You can quite easily get the signal from users of your MVP that they are not interested - when actually it's just that you have a crappy MVP.
Besides that, your original comment was not about building an MVP, it was referring to a full product. That's what I was referring to with "months" and "thousands"
1) Get them to agree [or disagree] that the problem exists.
2) Explain your solution and get a reaction.
You should already have some idea of demand before you write a single line of code (other than the code they wrote for this simple page)