We can help to incorporate a Cyprus companu within 2 - 3 weeks it is very slow compared to some other jurisdictions but thats part of the game.
If you can accept the company's name, and structure i.e. nominees, authorized share capital etc. then it will be much faster to buy a shelf company / dormant since you will received the corporate documents for the company as soon as payment has been received and you can start doing business with the company almost right away.