Is it possible to bypass the two-year foreign language requirement for a university by electing to take it during your time at the university?
No (although there may be some colleges that make exceptions). If a college asks for 2 years of foreign language in HS, that means they want 2 years of FL while you are in HS.
Keep in mind that many colleges, in addition to requesting FL study in HS, also have a FL requirement as part of their own graduation requirements.
Read the pinned post about FL on this page.
You need them to enter the university then add the college semesters in addition to that.
However if you’re a rising senior who’s only just realized that, you can take foreign language 1+2 at a community college during the year, as that counts as levels 1-3 in high school.
Some schools (which have more slots than they can easily fill) may allow you to make up a course or two after admission. But you’ll need to ask at each school and don’t expect it at selective schools.
Community college is your option to make up classes otherwise. One semester of community college equals one year of high school credit. You can take classes during the summer between high school years as well.
Requirements are meant to be completed before applying to the college. As part of the evaluation of a student’s academics the admission officers want to see that an applicant can succeed in the study of a foreign language. Of course you are free to apply to a college without meeting the requirements, but your application will be at a disadvantage.
And as noted above a number of colleges require students take additional foreign language coursework as an undergraduate.