You can play coop right from the start.
The controls are written on the website, but here they are again:
Player One:
[W][A][S][D] : move
[Space] : jump
[E] : interact
Player Two:
[🠔][🠖][ 🠕 ][ 🠗 ] : move
[J] : jump
[I] : interact
Gamepad controls:
[Analog stick] : move
[A] : jump
[X] : interact
Have fun!