There are some group quests on Argus, so while you can do it at level 45, it will be a lot easier if you’re at least level 50. (At 50 you get a moderate over-level bonus in Legion content which helps.)

First, the character should do the Legion intro. Pick the Broken Shore option from the Warchief’s Command/Hero’s Call board.

Once you’ve moved Dalaran and turned in “In the Blink of an Eye” an NPC for your Order Hall will track you down in Dalaran to start your Order Hall campaign. (It can take a minute or two, and it can help to move around Dalaran to trigger them.) Follow those quests until you’ve reached the point where you can pick a zone to quest in. (While technically, opening up the order hall isn’t required, not doing so can sometimes cause weirdness with other quests, so I find it worth the time.)

Unlock world quests by completing Uniting the Isles (required level 45) 1. (If it doesn’t pop up automatically, Khadgar will have it in the Violet Citadel.) If it’s your first character through Legion, you’ll need to do the “hard” version* of the quest where you get to Friendly with each of the 5 zone factions. (If you’ve done it before, you’ll get the easy version which you can just turn right back in.)

Once world quests are unlocked, go to Krasus’ Landing in Dalaran and Khadgar will have the quests Armies of Legionfall and Assault on the Broken Shore. (These are the only quests you need to complete here, it's your chance to get more Gold WotLK.)

Once you’ve turned in Assault on the Broken Shore, then you can go back to Khadgar in the Violet Citadel to pick up “The Hand of Fate.” This starts the Argus Campaign 2. You’ll need to do most of the quests there. The quests involving the mission table are not required so you don’t have to worry about leveling up followers.

*If you need to do the “hard” version of Uniting the Isles, you can pick up the starter quests for Azsuna (Court of Farandis), Val’Sharah (Dreamweavers), Highmountain (Highmountain Tauren), and Stormheim (Valajar) from your order hall scouting map. The 4 “leveling” zone reps can be done starting at level 10. For Suramar (Nightfallen) Khadgar will have the quest Khadgar’s Discovery or Magic Message to start it. It would help if you were 45 to start Suramar.