This is a very, very common failure mode of new entrepreneurs. As long as you don't have any customers, any promises, or any deadlines, you can focus on the best part of being a programmer: programming. Thus people often end up postponing the customer acquisition farther and farther into the future, until they run out of savings, or just abandon the project because the bright flame of new creation has dwindled.
Running a software business sucks. You have to mete out your attention extremely carefully, and without well-vetted potential customers to build things for, building things should be very low on your priority scale.
You can achieve most of your stated MVP goals with a sketch made in Adobe XD, with a fraction of the time spent.
I think of it as something that does the main purpose that looks entirely real (so has a domain and is responsive for example) but doesn't actually function. This can definitely be done in a similar amount of time as the XD sketch. Perhaps slightly longer but it'd look more real and therefore would be taken more seriously.
In fact its most important purpose is to save you from building something that does actually function.
Also plenty of clients will take meeting without an proof of concept. And this is especially true when you have a really good idea.
Makings the cold calls and cold emails felt a lot easier with an app built but at least in my experience didn't make a big difference in response rate.
Besides the fact that it'll be easier to visualize and present the idea to people, the act of building a proof of concept or a real MVP would be learning experiences themselves.
In fact thinking about what's to be included as part of the MVP and prioritizing to fit within a pre-set deadline would be extremely valuable.