I've been meaning to reply to this for a while. Since Christmas apparently!
It is possible to grow your way out of debt. Austerity is an option, but it's definitely the worst option. The growth strategy however depends on having a viable plan, but then austerity needs a plan too. It's not just a matter of saying 'spend less and my finances will improve'. If a publicly traded company said something like that their stock would suffer, even if they were deeply in debt.
Austerity is the equivalent of eating less to lose weight. Yes, you'll lose weight, but what you really need for your health is a good dietary plan and exercise regimen. (No, I'm not saying you're fat!) That usually includes austerity but it's not strictly necessary, the point here is to have a good plan.
The problem with simple austerity is often that it's treated like a whole solution all on its own. But if you think about it that view makes about as much sense as saying all debt is bad, regardless of circumstances . Yet businesses, governments, and you and me go into debt a lot for very good reasons. The difference is, like good austerity, we (hopefully) do it with a plan.
The premise of your scenario seemed to be that the debt was incurred for pure self-indulgence, but that's wasn't explicitly stated. So the flawed premise easily explains how you arrived at a flawed conclusion that all austerity is good.
Here's an example of bad austerity in the face of crushing debt; where many suspected the plan made no sense:
https://www.reuters.com/investigates/special-report/imf-greece/