If building a supersonic passenger plane with an existing engine was viable, it seems like somebody would already be doing it. Which means it's probably not viable, in which case Boom is an aircraft engine company first and foremost; once they have the engine, wrapping a plane around it should be the easy part, relatively speaking. Developing a new engine costs on the order of $1B, so the development cost for the whole plane would probably be between $1.5-2B. So they'd pay for that with their first 10 planes to Virgin, with maybe some money left over to change their name.
>If ... something ... was viable, it seems like somebody would already be doing it
This kind of thinking is useful as a first pass check, but one should not carry it too far. I would hope that by now the company has considered why no one has done it, and concluded that the obstacles are not insurmountable, and the prize in the end is worth it. Like so many other innovative companies, e.g. Tesla.
Also... "Somebody who would be already doing it" would have had to pass exactly the same hurdle.
Can you not just make the plane smaller and lighter and more aerodynamic and use a larger engine? You may also be able to show that current engines can operate at higher energy levels for longer?
Engine is generally optimised for max efficiency at a cruising speed. A airliner engine is optimised for transonic cruising, you can't just half the plane and double the speed.