Here are some ideas, but it will depend on where you live.
My oldest son had taken all the math and physics classes at the local community college by mid-10th grade, and he still wanted to take more math and physics. In our case, we opted to use an online mentor/tutor who worked with my son on advanced differential equations, dynamical systems, and a little real analysis. It was a very casual situation; he met with the tutor once a week (and sometimes missed a week) and probably didn’t have more that a couple hours of “homework” each week. My son loved the unschoolish nature of it.
The other thing my son did to keep sharp in math was to do math competitions. We have a great local math circle, so he did AMC10 and AMC 12, and AIME three times. He wasn’t motivated to really study much for the competitions, so he never made it to USAMO. He also did the local math olympiad, and did ARML, a team competition, three times (his absolute favorite). He also just read a lot of math books for enjoyment.
To help pay for the online tutor, we got financial assistance from a particular organization that supports highly gifted children, and offers financial support to families of moderate means.
As for physics, what we did was to contact a professor at the local state university which is about 10 minutes away. We did not contact admissions; my son went into through the back door. I basically emailed the prof, told him about my son, and he agreed to meet with my son. The prof allowed him to audit for free an upper division electromagnetism class for a year, and told my son to do it just as if he was officially enrolled. Because my son had the highest grade in the class, the prof invited my son to do physics research the following summer.
My son also audited an upper division optics course in fall of his senior year. (Same great prof) His prof even got him a job working at the state uni tutoring a student in electromagnetism. In the spring, his prof had him enter his research in the u/g research symposium even though my son wasn’t enrolled in the college.
The one stipulation is that my son was homeschooled/dual-enrolled, and thus had a much more flexible schedule than a student in a B&M school. I don’t know what constraints your child has as far as schedule, but auditing a class at a local university might be the way to go.
As far as competitive scholarships, those links above are great. For my son, he won full tuition scholarships at Vanderbilt, Harvey Mudd, and University of Pittsburgh. He won a full ride at UT Dallas. He didn’t win anything at WUSTL and didn’t get invited to compete for the full ride at Pitt. However, since our income is moderate, he got a lot of need-based aid at many of the colleges to which he applied, and he ended up at a college that meets 100% demonstrated need. It turned out to be very cheap for us because he also won a special Corporate National Merit Scholarship. Definitely check out National Merit opportunities.
BTW, don’t assume your son can get into MIT or any highly selective college. Though my son is graduating from MIT and gained admittance to all his colleges including several Ivies, we never, for a moment, assumed he’d get in. College admissions is more competitive than ever, and sometimes the process can seem random. Go in with an open mind and low expectations.