Sforno on Leviticus 16:24/ספורנו על ויקרא ט״ז:כ״ד

1ורחץ את בשרו, after he had supported his hands on the scape-goat. ועשה את עולתו, this was after he had first obtained his personal atonement, followed by the atonement on behalf of the people at large with the two sin offerings consisting of the male goats. Even the “scape-goat” is referred to here as a “sin offering,” חטאת, when we consider it had already been referred to as such in verse 5 where the Torah spoke about שני שעירי עזים לחטאת, “two male goats as sin offering.” Both of these procedures had to take place before the burnt offering on behalf of the people was offered. This was standard procedure, i.e. that the sin offering preceded the burnt offering. This point has been made in Pessachim 59.

2וכפר בעדו ובעד העם, the atonement required for inappropriate thoughts which ought to precede matters requiring “clean” (sin free) hands and a pure heart. Such a sin free state is achieved by means of the burnt offering.