The Jewish sacrifical system was created as a shadow of the salvation to come - so people would have been saved by following that.
Considering the lack of contemporary historical evidence for the existence of Jesus, the point is moot. People don't need "saving." That concept is an invention of religious figures to convince people to follow them (not a god).
Religions that predate Christianity, and even Judaism, by centuries or millenia had/have rituals that their followers perform to honour their gods; these rituals and practices are not to "save their immortal souls," but done because they bring them joy and peace, or whatever feeling it is intended to promote.