[Astromancer]

Try this idea, have a Turkish Peter the Great. Or at least a guy who could convince the Madhhab of the value of Printing. The Ottomans could have chosen to keep up with Europe technologically, they didn't. This was mainly a matter of the type of government the Sublime Porte ran. However, if the Turks, aided by Renegados (European converts to Islam in the pre-1800 period), were to embrace at least oceanic navigation and the printing press, the Ottoman state might easily have done as well as the Russians.

Place your great European reformer about a century ahead of Peter Romanov. If the defeat of the Spanish Armada and the Dutch Revolts caught the man's attention, and he got the power to lead the Ottoman state by the mid-17th century, the Turks might have enough lead time on Russia to take control of the Black Sea, the Caspian Sea, and Persia, before the Russians are fully in the game.

From here you can go several ways. Any of which creates lovely complex power politics for your game world.