If you wanted to get your body fit, chances are you would join a gym and/or hire a personal trainer. Getting your voice in shape to sing well is really no different. Chances are you would take singing lessons from a professional singing teacher or coach.
You can certainly get fit without going to a gym if you know what you are doing. So, can you learn how to be a vocal athlete without the guidance of a singing coach?
Professional singing coaches should be able to tell you what is standing in the way of becoming a better singer at the first lesson. They should be able to tell you how your voice works, and what issue(s) is possibly stopping you from improving. Then they should be able to show you some exercises that will instantly improve your voice in some way or another.
Has your voice been diagnosed? A great voice is usually a balanced voice. Working on that balance would typically need a professional’s ear and knowledge to get the best results. Once you know what to work on, and know that you are doing your exercises properly, then indeed, you may become a vocal athlete without the guidance of a good coach!