Switching to finance or quant career from software engineering

Hey, so I've been looking for a quant career for about a year now and haven't had much luck. It's something that I would really love to do and I think I would be really good at it (I guess everyone does), but the interview questions always catch me off guard (I once got a question that was only recently solved in a math paper and another that not one of my 3 math PhD roommates could do after several hours).

Anyways, I got a PhD in mathematics from a top 5 university, have done tons of studying in not-my-fields (algorithms, trading, statistics, machine learning), and have done a few projects in both C++ (I plan to implement my own neural network to play a simple game I created) and Python (machine learning/data science) but I'm just not feeling great as it looks like my dream of working in finance is turning into a nightmare. I've been unemployed since June and need to find a job quick for my finances and health. A friend reached out with an opportunity in software engineering (with a little bit of deep learning) at their company that would definitely be interested in hiring me, but I'm worried that I missed my chance for my dream job.

So, my question is, thus: is it possible to switch careers from software engineering to finance and how common is it? Any tips on how to do that? Or should I just give up hope now?