You cannot attend college (take classes for credit etc) and apply as a freshman, with few exceptions.
If your country requires you to be registered somewhere in order to be “recognized”, " have a card", “have health coverage” that’s okay as long as it’s purely administrative.
You can take non credit community classes (say, you volunteer in Uulan Baatar and take classes in Mongolian for foreigners or someone teaches you a traditional art or sport, that’s okay.)
If you graduated Spring or Summer 2023, you can take a gap year and be considered a freshman for admissions purpose.
Will you need financial aid?
Do you have stats? An academic record?
(NYU admits with Gaokao results, most universities admit based on your school record from grade 8 or 9 through 12 or 13, many want to see SAT or ACT results, especially for scholarships. )
What would you like to study?