Now that OP is asking, I tried looking this up at my local CC. Looks to me classes are open to anyone. You can get a certificate of achievement after completing the list of classes (from the school).
But at least in CA, https://ems.acgov.org/ems-assets/docs/Certification/ALCOEMS_EMTCertification_FAQ.pdf A person will need to be over 18 to to actually be able to work as a certified EMT (from the state).