The way you get to management is by having people report to you and then get a new job higher up on the ladder at another company (it is my understanding that promotions from within the company are difficult compared to hiring outsiders).
One puts in time in grade, switching projects frequently to build up the resume. Unfortunately, this makes institutional knowledge at the client companies not something that is preserved easily.
(anecdote: when I was laid off to be replaced by someone from India, the 12 years of how the system works was transferred in 4 weeks of 4h a day meetings, 5 days a week (that was painful)... keeping in touch with my old coworkers, the person who replaced me left 6 months later and explained everything about how my job worked and what they learned in just a few days... who left six months later and only did one day of information transfer)
So, switch companies, go from developer to sr. developer in a year (2x 6 month projects) to team lead (with 5 people reporting - another year or so) to architect (with 3 team leads reporting - another year or so)... and you've got a manager.
If someone is on the track "I want to be a manager", switching projects frequently and never actually diving too deeply into the project is probably the best approach.
The technical people are harder to find. They're not switching jobs quickly and so they're unlikely to get hired into the project that the client sees. Maybe they're tapped as a "work on this 25%" but I know how that goes... it means one week out of the month you're catching up on everything for that project and trying to fend off context switches before you're not thinking about it for another month.
For the technical people, many of them are able to find a visa and move to the US for some extended period of time. This contributes to a brain drain in India. Also the indentured servitude aspect of the H1B visa means that there is less mobility and again, its harder to meet these people in random places. They do exist - and I've worked with a number of them... but I've worked with far more people who are in a position for six months to a year and then moving on to another contract at another contracting company.