This sounds like a very unlikely way to make any progress.
If neither your degree nor your work experience are engineering-related, there's really not much point in taking the FE exam.
If by some miracle, you can take and pass the exam, it's not really going to open any doors for you.
I have known people who didn't have a degree who worked in engineering or related fields for years, and for them, that would have made some sense.
One of the challenges of the FE exam is that it covers a very wide range of topics. If you hit it fresh out of engineering school, you're in pretty good shape. If you get into industry and work in a very narrow field, you tend to forget all that stuff you never use, so it's actually harder to do it after 10 or 20 years than it is to do it while the topics are still somewhat fresh on your mind. If you've never taken any of the subjects to begin with, I'd say you're in a considerably worse off shape than all the people who learned it and forgot most of it.