The program should have started by now, so we’ll probably miss the first half.
We have a loan word プログラム from “program” in English. But we don’t usually say プログラム in this usage. プログラム should be replaced with 講演 (こうえん), 上演/公演 (じょうえん/こうえん) or 上映 (じょうえい). 講演 is for live talks to enlighten audience such as key note speeches and political debates. 上演/公演 are for live entertainment such as theater plays and music performance. 上映 is for recorded works such as films.