No, that is not feasible. Without formal training, your only other option for making money in trading is to simply buy and hold your positions. Professional training doesn't always entail receiving instruction from an expert; instead, it refers to continually honing your own skills using any profitable trading strategy and making numerous trades until you are confident in it. The only method to profit from trading is in this manner.
What you mentioned as professional training is informal training or self-study. So yes, it is feasible to become good and earn decent returns in trading without the need for a professional expert.
Most people I know that are good traders learned it for free and without experts guiding them. It's more on the willingness and dedication to spend time and make effort in order to learn the many strategies and techniques in trading. Because everything can now be seen on the internet nowadays if we only have the diligence to look for them.