You can become a Jedi if you should find a trained force user who is willing to test you. If you are found to be force sensitive, and only then you can start training.
Now, the problem you will encounter is:
Finding a trained force user who's willing to test you. They are usually not moving into public just because someone wants to be tested. With Out Of Faction Arrest/Execute around they are somewhat careful.
For the notes, it's easier to assume that your character is not force sensitive, because, in fact, it's unlikely that you are indeed force sensitive.