Most applications are cold applied right now just because we don’t have too many connections here. We’re trying to crawl our networks and see if we can find some intros.
I don't recommend limiting yourself to networking with only people you know, especially when the company you are interested in applying to is large (in terms of head count). Once you find a company of interest, reach out to people at the company via LinkedIn. Just ask questions about initiatives that they are doing. Ask intelligent questions, ones that show you've done some preliminary research on your own. After a little back and forth, mention that you are interested in applying. Ask what the best way to apply would be. At this point, ideally, they respond with a "let me forward your resume to our in-house people." If they say you can apply online, you can slightly nudge by asking if they think a referral would help the process. Hopefully they bite and offer to refer you. If not, you can try reaching out to someone else. At big companies, people freely hand out referrals since they get money if you get hired but suffer no penalties if you don't.
When I tried this method on LinkedIn for my own entry-level job search, I would probably get responses 10-20% of the time. Just giving you that number so you get a better idea of what success looks like in this situation.
