My neck is 361 and I have played a lot but not at a super grind rate (have a 120 alt who is total ilvl 337 to go along with the character who has the neck for example). Just do every Champions WQ possible every single day, as many table quests as possible for Champions (a bit rng based on what Preach has said, I feel I have had a middling amount of them), do all weekly Mythics, the weekly 2,500 azerite from Invasions, and maybe another 50ish heroics thrown in across all that time, plus w/e azerite I pick up from other world quests (did every Legion one possible until day 5.5 when I unlocked the dungeon, for example). I have friends 1.5 Azerite levels above me, but the big boost comes from Champions rep and once you hit Revered you are most of the way to that high ilvl neck.