That's a good point, but I think people have a lot more connections than they realize
Chances are good you're acquainted with 50+ people, and if each of them is acquainted with 20 unique people, that's 1000 people you can contact through a few weeks of hanging out and chatting
Professors often know relevant industry people in town, too
Worst case, you can hop on here or blind and ask for referrals. Some random dude cold-mailed me before and asked for a referral to my company. I chatted with him a little to make sure he wasn't completely insane, then passed his resume on to a relevant hiring manager. I forgot all about it until I noticed that a $3000 referral bonus showed up in my paycheck a few months later
Not necessarily, but it does make it easier if you have that opportunity. Places like Tata are good for someone with no connections to get a footing.