I went to a non-top tier undergraduate school. I made efforts--at big companies as well as the one I founded--to recruit from my
alma mater. I ended up defaulting to NYU, Harvard and Stanford.
Career services at non-top tier schools are shit. Once, as a personal favor, I offered to help a company with a well-known CEO recruit from my state school. When I brought it up with a dean I knew, career services got mad. They said I should have gone through them first. Guarding their gatekeeping function was of greater concern than doing their job. They then suggested this CEO come to their fall freshman career fair. I said no, it's a high-profile company, they'd prefer if you curated a list for them. (MIT and NYU, amongst others, do this.) No response.
Consider, too, that 90% of recent-college graduate recruiting (in finance, at least) is less about finding brilliance than finding someone who won't make dumb mistakes. The Ivy League produces a consistent product. They hold no monopoly on genius. But the variance around others' outputs is too high for a young firm.
All that said, I never turn down an outbound email. (It's how I broke into the industry.) I also think it's important, as your firm develops, to keep an eye on broadening recruiting.
Closing note: in response to recent news, I started thinking about our workplace's gender diversity. It's bad, and it matches that of the schools we recruit from.