Over that first year there it was basically the Klingon Rite of Ascension. Fighting fires and trying to keep the company afloat. I had no backup/mentors and if I failed then the company was done. I was near tears (or privately at tears) at a few points from frustration and stress. In the end I think this experience made me a better person for it.
First I was forced to learn how to manage stress. This was a big one and one I had never mastered before. Next I need to be able to juggle and prioritize actual company needs, not just what people told me to do. I couldn't spend all my time fixing things when our customers also needed our product to work. I also handled much of the customer support at this point because most of the issues were software related.
In any case, in the end I pulled the company back from its instability. This gave me a good amount of confidence that I am a good engineer. That no matter what gets thrown at me I can fix any of our problems and develop new systems. Even if I need to outsource some of the work to people who are better at particular platforms.
This probably isn't a healthy way to overcome impostor syndrome, but its how I did.