My high school won’t put a CTY course on my transcript, but can I still earn college credit from a course and, if so, how do I get the credit?
Depends upon the college. Generally, no. Some colleges will have a departmental challenge exam for credit. Penn and MIT comes to mind. Others want you to learn their way of higher math and offer an honors MVC class. You would need to check with each college.
Unless a multivariable calculus course is an actual college course, it will not be accepted for college credit. As noted above, some colleges’ math departments may offer advanced placement by exam or some such.
Fwiw, CTY will issue a transcript as an accredited K-12 school. They will also issue a grade, but I think you need to request this in advance and I don’t know if it applies to self-paced courses.
Whether a school accepts this will be on an individual basis. Testing out is probably the most likely option.
Also consider just taking the course if it’s important to your planned major.