So, can you get DNA without AUs? Yes! You can get most DNA without them.

Sources:
Blue DNA - Snap
Green DNA - Fruit machine
Pink DNA - Rapunzel
Red DNA - Raffle
Brown DNA - Millionaire's Lodge, smuggler
White DNA - Extract Enipiah Prize
Black DNA - Recycling Centre
Purple DNA - Random event
Grey and Orange DNA - Pirate ship.

You were able to get yellow DNA for promoting marapets, though that currently isn't working right now.