The group was likely engaged in combat with the Covenant in the Battle of Earth, as the video's visible factual text says the group only has 2 ships out of 8 remaining. The group requested rearmament since its readiness level was critical. Misriah armory factories on Mars then were shown mass-producing equipment for the Battle Group, which likely not only uses its ships for space combat, but also assists Marines in ground engagements since the production of Marine vehicles (Warthogs and Pelicans) and weapons (Sniper Rifles, Battle Rifles, and M6G Magnum Sidearms) are shown.
Specifically, the Marine unit (of unknown size) called S4/BAG/2/5 could be assigned to the Battle Group, as it is seen in the video. The Marines themselves are seen in the trailer preparing for combat, and at least one, (Benjamin M. Nunez), is not a recruit, though the other Marine(s) pictured likely are.