My team and I have started a career accelerator for college students who want to work at tech companies in Silicon Valley. We're doing this for free for students. We've built a solid network in SV, including the former president of Google Enterprise. Applications are now open!
You're right that there's a pretty big demand for talent. Many talented college students have the skills to get into high level tech companies, but they simply don't have proper connections. We want to make it easier for college students to network. Also, recruiters have a hard time finding highly talented college students. We help prep the students for interviews, restructure their resumés, and give them a serious amount of connections. Students don't have to spend time looking into a few places to work. We can bring them tens of job offers since we have a solid network in Silicon Valley. To sum it up: college students get to spend less time searching for jobs, and more time studying/getting better at their craft; while we bring them the jobs and prep them. I like the questions! Keep 'em coming.
University recruiters are rare to find outside of the largest companies. But let's say yes, you want a job at Google or Facebook. Why not just go to their recruiters? You actually should do that if you are confident you will make it in. One thing to consider is that these recruiters look over hundreds of applications every day when recruiting season is high. We look over quite a few as well, but we only select the best from our batch. After that we personally get to know them, help them in every possible way, mock interviewing/challenges, resumé cleanup, and most importantly, a lot of connections to hiring managers, VPs, and a good deal more. We are somewhat of a hyper-focused team who looks after our students.