You'll need enough time in your enlisted contract to complete OCS. Depending on your ETS, you may need to extend for a year or two.
Branching ultimately revolves around the needs of your State. MI branch doesn't need many lieutenants, although it needs more captains, so you could serve in another branch for a few years and switch at that point. You may also consider staying enlisted, and becoming an MI warrant officer. That's a harder path, but we're always short of MI warrants. Talk to your State OSM of command chief WO about that.