What I read about it suggests that freighter travel can be (and often is) booked a year before the departure date. It's not an absolute rule, and some agencies do offer “last-minute” trips, but there is some paperwork to be taken care of (insurance, medical check-up, vaccination) and most people seem to plan such trips well in advance so that some routes are already fully booked for 2015.
From South Asia, you have several obvious options to reach the US, often with a change of ship at some stage (you do need to plan for a week-long layover because the schedules are not guaranteed):
Those are just examples, there are many possibilities and most agencies should be able to piece together a route for you. You would be looking at something like a couple of months of travel in any case.
But the biggest problem is that I read in several places that India does not allow passengers to embark or disembark on cargo ships in the country. So, even though many ships do travel to India, you first need to go somewhere else like Sri Lanka or Singapore, quite far away from Mumbai, to catch a freighter.