A large part of AN124 and IL76 pilots are ex-military however there are many pilots with civilian background as well.
One of the biggest problems you may face is Russian is used as a working language in a cockpit, also all docs/manuals/training/etc are in Russian. Yes, there are docs and training available in English but it is for a group training for a foreign customers like Indian Air Forces, I don't think any commercial operator would even consider to arrange it for you.
Also you should be aware that IL76 jobs are very low paid.