Third Party photon pun 2

How can I make the player press 'play' on photon pun 2 so that everyone is thrown into one room

 

You first do the matchmaking. When players are in a room together, they can send each other messages / interact. To actually start the game by loading a specific scene, you can use AutomaticallySyncScene (explained in the PUN Basics Tutorial). Alternatively, you can send an RPC to everyone or set a Custom Room Property.
The PUN 2 package includes the "Asteroids" demo, which implements everyone signalling a "ready" state and then starting the game on the Master Client.