First of all, there is a difference between rares and upgraded cards (you probably know that, but just to be clear).
You can't win anything from lvl 0, because you get no spin.
I'm pretty sure lvl 1 and 2 use rares (weapons), which means technically you should be able to win them, but you only get to spin once or twice per win, respectively.
The reason most people grind AI3 to start is because you get 3 spins (3 chances to win a card) per win, and speed decks can get through matches quickly (thus giving you a lot of chances to win cards in a short time). You can win weapons, Miracles and Squids from AI3.
You also get 3 spins for winning a match against the Top 50. You can win any card from the deck you played (weapons, shards, etc) except Nymphs, and you cannot win upgraded cards.
You get 3 spins for AI5 as well. You can win weapons, Miracles and Squids but not shards. You have a small chance (like 2%, if I recall) to win upgraded cards.
You get 3 spins for False Gods. You can win all the same cards as AI5, but ALL cards won are upgraded.
You can only get Nymphs from the Oracle. Also, I think the odds of winning a weapon may be better in AI3 because their decks are smaller than AI5 (30-40 cards for AI3 vs 60 cards for AI5). Therefore, they have a better chance to be selected for a spin.