I recently published my undergrad research in Information Theory at this conference called IEEE ISIT 2022. I looked up the published paper, and my name is at the first and then the other authors' names follow. Does this mean I am the first-author of the paper? Or what kind of author level do I call myself? It was a paper written primarily by me but my professor and two other students also helped.
Congratulations on your success.
If you look at the conference proceedings, you will find that a slight majority of the papers have authors listed in alphabetical order. This suggests that some teams follow the Mathematics convention of alphabetical order and others follow the Computer Science convention which embeds information on the role of the authors in the listing of authors.
If your name comes alphabetically after at least one of your co-author's names, then you are a recognizable first author, you are the student that did the work and to whom more of the credit goes. As it is traditional in my part of Computer Science to (almost) always list students first, it is not apparent from the author listing that you had the principal idea. If not, then you are the first-listed author with no information about the contributions encoded in the list of authors. "Ontologically", you appear to be the first author and can call yourself this in a statement of purpose. However, I would be careful about not appearing to be bragging and instead give the same information that you gave us in your question. With other words, I would advise you to relate your success in a statement of research interests or something similar and not make a big deal about what type of author exactly you are, even though, in fact, you appear to have been the primary author.