According to the Mishnah (112b) until the Tabernacle was established in the desert, sacrifices were brought on bamot – private altars – and the sacrificial service was performed by the bekhorim, the first-born. After the Tabernacle was erected sacrifices could only be brought there and the sacrificial service was performed by the kohanim – descendants of Aharon haKohen. According to the Mishnah, the commandment to sanctify the first born was given at the time of the Exodus from Egypt (see Sefer Shemot 13:2), and the first-born redeemed themselves from Temple service later on, as described in Sefer Bamidbar (3:12). According to the Talmud Yerushalmi, the reason for this was the participation of the first-born in sacrificing to the Golden Calf, something that the members of the Tribe of Levi did not do.
The Gemara on today’s daf quotes a baraita that offers an alternative approach to this question. According to Rabbi Assi, the first-born sacrificed for just one day, in conjunction with the experience of Mount Sinai. Thus, the “young men” who brought sacrifices (see Sefer Shemot 24:5) at that time did so for just that day, in the third month following the Exodus. From that time on until the Tabernacle was built – in the first month of the second year following the Exodus – Aharon’s son’s Nadav and Avihu served as priests. During the consecration ceremony of the Tabernacle, Nadav and Avihu died under tragic circumstances (see Vayikra, Chapter 10), and from that point on it was the rest of Aharon’s sons and their descendants who were responsible for the sacrificial service in the Temple.
Rashi has an alternative reading that seems to indicate that the “young men” in Sefer Shemot 24:5 did not actually bring the sacrifices, but represented the people as onlookers to the sacrificial service that was performed. According to this reading there is a possibility that the first-born never served a role in bringing sacrifices.