With all the classes, you need to engram to unlock it as a secondary class. If you don’t choose it as a starting class, you have to get the engram in game like you normally would.
The real question is why are you starting a new character? Why wouldn’t you just pick a new class and reroll the campaign? It scales to your power level, which is based on your class levels and your weapon levels. Picking a new class and an unleveled gun will feel like a new game but you won’t have to go find all the engrams again and you’ll have the benefit of your unlocked traits and interesting guns and stuff.
EDIT - Regarding spawning the blood moon, the technique I read was to spawn into a different zone and back again but NOT the Ward. Worked fine for me… just takes patience.