If you want to avoid going through Russia, that's a unique challenge. The southern route, the old Hippie Trail is not passable and the northern, long route through China is very hard without passing through Russia. Let's look at the map!
From North to South (slightly West to East too) you have Russia, Kazakhstan, Turkmenistan, Afghanistan and Pakistan. If Russia, Afghastanistan and Pakistan is out you need to get across somehow the other two. You can forget Turkmenistan with public transit, you can't get in, you can't get across and you can't get out. Everything else is peachy :)
So then let's look at Kazakhstan from Turkey without Russia. If we had a ferry from Baku, Azerbaijan to Aktau then we would be all set. Does it exist? This is where things get challenging it exists but barely. From there it's easy just very long: According to Rome2Rio you can take trains to Almaty, and from Almaty in a mere five days across China http://www.rome2rio.com/s/Almaty/New-Delhi you can get to New Delhi.
OK so we need to get to Baku from Turkey but that's easy http://www.rome2rio.com/s/Istanbul/Baku there's a direct bus.