I know this is a dumb question, but how do you determine initiative order for games with no Imperial presence? Where does scrum fit, and what about same faction games? Thanks.

The vast majority of players use some variation of the tournament method of determining initiative. In short

If the points are not even, the person with fewer points in their squad may choose whether to have initiative

If points are equal, randomly determine one player to have the choice.

If, for some reason, you don't want to do that, the scenario in the IG-88 expansions lists the initiative priority as imperial-rebel-scum.

For a multi-player game, good luck, it can get confusing fast.