Essentially, if you don't have at least a master's degree in the field you want to teach in, neither a 2-year college nor a 4-year university will onboard you as any kind of teaching staff. The exceptions lie in the TAs because they are chosen by the professor of the course as his/her assistants. Furthermore, they tend to also be enrolled in master's-or-higher programs and have more advanced knowledge than the people that they would be teaching. Because they are working for the prof, they also get tuition assistance through the university and can overlook a student's visa status as international students typically can't work outside of university-provided jobs. Even those have to be directly through the university.
Another potential exception that could be made is if you are highly experienced in a field or you are a native speaker of what is considered to be a critical need language. With these, there would be extra steps involved (such as the speaker of another language being asked to pursue a higher degree), but with the right university and/or skillset many things are possible. I'm pretty sure that the only qualification my business Chinese instructor had was that she was actually from China as she could not speak any English. Thus, as a Chinese major, I and another student ended up translating for her in class and tutoring everyone else after.