Not only can you pistol start each level (it's pretty commonplace), it's actually possible to complete most levels in "pacifist" mode, where the player can't harm any enemies. Decino did a 3-parter on this:

Part 1: https://www.youtube.com/watch?v=PTvTsl3x2qY

Part 2: https://www.youtube.com/watch?v=mbRKER3HtAY

Part 3: https://www.youtube.com/watch?v=nlk022mO83k