It wasn't Stanford, but when I was in your shoes I also had my sights on a dream "reach" school that my guidance counselor even told me would be a long shot for getting into. But I had done my research about the school and what it offered (like it sounds like you have) and had visited the campus and met some students, and knew that it was a great choice for me, if I could get in. If Stanford has so many attractive opportunities to you (your desired major and a robotics club), I encourage you to apply - as they say, you miss 100% of the shots you don't take!
One thing that I think helped set my application apart from the thousands of other applications was that I made as much of an effort as possible to connect with people at the school, to show how interested I was. If traveling to Stanford on a campus visit is financially and logistically possible for you, I would suggest visiting the school and trying to speak with someone in the admissions office - or, even better, ask the admissions office to connect you with a professor or current students in the mechanical engineering program to learn more about that program specifically! Achieving your highest possible scores on the PSAT and SAT will certain help your application, but if you can demonstrate that you have done your research and taken the time to really "get to know" the program you are most interested in, and if you can express why you belong at Stanford after all that research, I think that would go a long way when they are evaluating your application for admission. Good luck!!
Kelsey recommends the following next steps:
- Keep studying for standardized tests!
- Contact university admissions department to request more information for prospective students
- Connect with current university students or professors who would be willing to talk about the program you are interested in