I'm having the same issue. There's no contracts or anything and no prompt to even start the game
Hi Nerae, so first thing: hit the "p" key to get out of the contracts window.
To find contracts, a source and a destination need to be selected. When in the contracts window, leftclick to select a source, and shift-leftclick to select a destination. Rightclick will rotate the map around.
I'll come out with a game guide this week that goes over these features more. Keep in mind the whole contracts thing is very early in development.