How long should it take to make the mvp?

My mvp took about 3 months. I was working about 1-2 hours everyday. I also have a full time job. I hope customers will pay but I'm ok if they don't. I don't see it as a waste because I learned a ton and the project will also be on my resume. I consider it a win win. Best of luck.

mmm...
There are a few important points:
✔️9/10 business fail - plan to make 12 (Robert Kiyosaki/Rich Dad Poor Dad, used to say you need to make 10, but I think some slack is good)
✔️ Validate fast - Validation should proceed MVP. And there are different steps you can use before you commit to an MVP. Like Tim Farris in 4 hour work week and Lean Startup/Eric Ries I believe, sales page only and paid traffic to it, to see if people will pay. (1-2 days for the landing page, 1 week traffic testing)
✔️ Do things that don't scale / YC - your MVP might be just the wizard of oz type, where a monkey runs in the back and does things manually. The MVP is not a technical POC, you're not proving your building/technicals, you're proving the business commercial viability, focused on user interest and pay (hopefully)
✔️ Constraint your time to increase focus - "Work will expand to fill the time allotted", "ship early ship often", "perfectionists never get anything done", "Make a bad first draft..".... make sure the focus is on coming out, not on raising a baby.
I think, if you could come up with how much time you think it would comfortably take you, cut that in 3 and set that as your time constraint, not so you work yourself to the grave, but so you will make the hard choices about cutting out the scope. (scope creep is a huge enemy)

At least these are the point I'd use to back the statement, due 1 month, could be arbitrary, better use 2 weeks 😈 (there is an old joke that everything "takes 2 weeks", it's the most common estimate and a common agile cycle)

do what you have to. I work too, got lil kids, and I'm going to have to utilize machine learning too, so yeah, I expect mine to take about 3 months. it's not a sprint. if you're truly solving a problem, then what does it matter if it takes 2 weeks or 4 months? just do it.