Meet Johnson early
From Halopedia, the Halo wiki
It is possible to sword-fly into the scarab. When you are about to come through the door revealing the Scarab, make sure you have a Covenant carbine and an energy sword. When you come through the door, use a Brute to sword-fly into the Scarab. Once you enter it, Johnson should follow, equipped with a plasma pistol.
This can also be achieved by using one of the Karo'etba-pattern Ghosts and simply speeding out of the last doorway and climbing in before Johnson does, using its legs as steps. It may take one or two tries to achieve, but you should usually have saved a checkpoint, and you can simply revert it if you fail. Also note that you cannot leave the Scarab after you have done this.