If you want to avoid going through Russia, that's a unique challenge.
You can try the Turkey-Iran-Pakistan-India route as described https://en.wikivoyage.org/wiki/Istanbul_to_New_Delhi_over_land here. It's very detailed; your challenges might be getting the right visas and the Iran-Pakistan border.
Or you can take a more northern route. 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 (and they are, you can't get into India from Pakistan and also there is no public transit from Iran into Pakistan) 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. If you can give up "land only" for this hop, Azal flies this which is often <100USD (airport codes: GYD for Baku, SCO for Aktau). I would say it is well worth to be across in an hour instead of a week and that doesn't include the challenges of finding the port and the horrible conditions on such a cargo ship. Of course, if you have. say, medical problems with flying then good luck with the ship.
Edit: since 2016 October it is possible book the Alat-Aktau ticket online. It confirms it goes from Alat and not Baku. Same page can be used for Türkmənbaşı.
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.