I started the campaign fresh, reverting to drawdown 2035 and playing on veteran. The issues I found are from playing through the campaign, not using the campaign cheat or hitting "replay"
Edit: I also tried launching the mission via the strategic map, but encountered the same issue.
Edit: Clarified the description after realizing that it was Alpha team in the truck and not Bravo, and remembering that you are supposed to board the truck, although the order is never given.