(I know I'm not IlyaShpitser, but better my reply than no reply.) I have several papers on the arXiv, and the very first time I submitted one I remember it being automatically posted without needing endorsement (and searching my inbox confirms that; there's no extra email there asking me to find an endorser). If you submit a not-obviously-cranky-or-offtopic preprint from a university email address I expect it to sail right through.