Interesting question, you do have a manager, the VP of Software, if they are not coaching/mentoring you and helping you grow into your managerial role they are putting both your career and the company's future at risk. Just saying.
The first thing to remember is you will always "be personally tasked with building out the product" and you will be doing less and less of the actual coding, but you will still get fired if the product fails big time. In theory the extra risk come along with extra pay, since this sounds like the first time you're doing this I'm guessing you may find you aren't being paid commensurately with the risk you are taking.
As you become senior leadership, your task is to look further and further ahead in time and try to anticipate, and have plans for the various situations that may arise. Given that those situations will have various chances of actually coming to pass, those that are unlikely you can just sketch out an idea for a plan, those that are more likely you need something more detailed. One of the secrets of being a good leader is that while it may seem like you "pulled a great plan out of the air when this thing happened", its really that you had already considered weeks or months ago what you would recommend if that weird thing happened.
As you get closer to the top you will have to include business priorities as part of the "weird things that can happen you have to look out for." and to understand exactly how the company is generating value using the products or services your team is developing or providing. Nothing is more frustrating to a brilliant engineer than to deliver a beautiful architecture and product to a company that cannot use it in their business when it is delivered.
You should probably have a discussion with your boss, and your boss' boss in the same room talking about what you're going to be working on and delivering with your team. It will help tremendously down the road. That is also a good time to ask for training resources as your boss' boss will be eager to fund them if you are being successful and that will encourage your boss to actually provide them.
There is a weird point you can get to when you realize that you're boss is afraid of you, depending on your boss that can be very uncomfortable.