The rules are not crystal clear on this, i.e., they don't explicitly say to skip the turn order. Here's what they do say.
Under Game Setup:
For the first turn, the players choose the turn order randomly.
Then, each player, in turn order, chooses how to allocate 3 points among his pyramids, choosing either of the following combinations: 1 / 1 / 1 or 2 / 1 / 0.
Under Step 4 of the Night Phase it states after how to normally determine turn order:
For the first turn, the turn order is randomly determined.
I read these together to mean skip step 4 of the night phase on the first turn. The first part mentions that the order for the turn is determined in a special way.