why do you want to do it professionally ? you have something special (you are math genius, have talent or extremely strong motivation and belief in your intellectual capabilities)? do you know/ feel you can outperform other market participants ? because it is well paid ? because it is one of a socially respected professions, a prove for others that you are "somebody" or just generally like the idea ? Ask yourself, just for your self-awareness, because this is important.
Anyway you firstly must be aware nobody will pay you a cent/penny/eurocent if you don't earn real money on the market. I don't know how exactly it is with investment banks but there you must have an excellent academic background and serve there for some longer time as a support or something, that probably is one of the ways. But thousands of people meeting those requirements can't get there.
I was offered a position as trainee in a trading firm with quite large backing, because I knew where I came and what for and I felt on interview more like partner in business than someone who wants a job. I was interested in trading since I was 19, studied business management , but wrote dissertation about technical and fundamental indicators , I was trading forex at home , testing technical trading systems using excel, had huge drive to do it not because I "wanted to be a trader" but I felt passion in the subject and I feel it when I do my work now. so I'm working for a firm because I was deeply into it, started to mold myself into that role early enough. Never aimed to do it professionally, I always wanted to do it for myself, I just sent a cv there.