If I play creatures with no effects that don't start a showdown, can my opponent play a response like Gust?

Ruling: If you play units with no effects and no showdowns or triggers occur, there is no priority window for your opponent to respond.

Nuances:

• If you're playing Annie, Dark Child or Volibear and one of the units you play has 5+ might, there may be a priority window
• Units with activated or triggered abilities create a stack that has a reaction window