The purpose of the T32 is to fund institutions to fund researchers. As a student, you do not personally apply for a T32. You would apply to a T32-funded training program, and the program director (or program steering committee) would assess whether or not you are a good bet. The program director will be looking to appoint people who are committed to a career in research and who plan to remain on the training grant for 2+ years.
So if you are asking about how to improve your chances to get into a T32 training program, then you basically need to show that you are serious about research. If you already have a lot of research experience, you should be in good shape. If you don't have any research experience, or if you want to get more research experience under your belt to improve your application, then you will need to find time to do research during medical school before you entre the T32. Most medical students who take time off during medical school to pursue full time research (through a T32) before residency training generally do it after completing the MS2 or MS3 year (i.e., finish MS1-MS2, do full time research for 2-5 years, and then come back to complete MS3-MS4). So if you want to show that you are serious about research, then you basically have 2 years to do it: find someone who is willing to hire you as a part time research assistant (and full time during the summer between MS1 and MS2) and give it as many hours as you can without compromising your grades.
T32 training programs take both predoctoral and postdoctoral students. So doing it during medical school (i.e., taking time off) is only one way to do it. You could also go straight through medical school, then complete residency (and clinical fellowship), and then apply for the T32 during fellowship. Same rules about boosting your application apply: basically try to get as much research experience under your belt during medical school, residency, and fellowship to convince the program director that you are a good bet.