Say hello to the mongol empire!
Basically, your ahc happened IRL and especially under the reign of Kublai Kahn.
As far back as Ogodei, it was common for mongol rulers to transport learned individuals across the world to where they were most needed, most commonly between Islamic and Chinese civilisations but also Europe for its stone and steelwork and clever use of glass.
Now India is interesting in this case, never having been properly conquered by the mongols and thus not fully privy to their expansive network. How you would get both parts of Europe and India to be conquered is a challenge, namely as in the court of Ogodei, the descision ultimately went in favour of attacking Europe.
Somehow gt both, and you will get more European stuff going to India.