No, if a monster outside Tokyo rolls smash (the attack symbol) when no one is in Tokyo, no one takes damage.

This is supported by the following rules:

• On page 5, under "Enter Tokyo," it states:
  "If no one is in Tokyo, your Monster takes control of Tokyo. Place it on the board."
• On page 4, under "smash," it states:
  "If you are outside of Tokyo and you roll smash, wound the Monster who is in Tokyo."
• Also on page 4:
  "Since no Monster starts the game in Tokyo, the Monster who plays first does not cause Monsters to lose [life] with smash."

Since the rule specifies that only the Monster in Tokyo can be wounded by a Monster outside of Tokyo rolling smash, and if there is no Monster in Tokyo, there is no target to wound. Therefore, no one takes damage.

Source: pages 4–5.

Source: Core Rulebook (pp. 3, 4, 5, 6)