I've done intrapeneuriship a few times. You don't need to just convince your CTO, but your whole executive team.
Your company has existing goals, revenue projections, hiring plans, budget allocation, headcount allocation, etc that all of your company leaders have agreed on.
Asking to build an MVP requires not only the cost (budget, headcount, etc) to build and launch the MVP, but also an opportunity cost as less resources are being used towards the existing plans.
When I've worked on new businesses, we first get buy in from the top execs, but the next step is to work with finance on budget and revenue projections, and with departmental VPs on finding headcount to join the new team.
This might be a lighter weight process in a smaller company, but my point is that it's not just your CTOs approval you need, though your CTO could be your champion to help persuade everyone else this is worth doing.