Yes, the default is to tap for colorless mana, if nothing indicates otherwise.
If a player wants to cast
Polukranos, World Eater using a Forest, a Llanowar Wastes and two lands that can't produce G, then they clearly had to use the 2nd ability of
Llanowar Wastes, and need to take 1 damage; if they don't announce that change in life totals, we need to step in (GRV for not resolving that ability correctly).
d:^D