Getting an Interview at a Firm With No Contacts

I'm three years out of school looking to break into IB with solid accounting/corporate finance experience. I've been building out my network over the past few months and things are going well. I have solid contacts at 10 or so firms in my city and I'm confident that I would be able to get an interview if an opportunity came up at one of those firms. HOWEVER, is there anything I can do to get an interview when I see a posting for a firm from which I don't have any contacts in my networking pipeline? I feel like emailing people at the analyst/associate level is a waste of time because it's just too late and they know you're just going to ask them for an interview. Should I try to find out who works in HR and reach out to them? If so, what should I say? It's happened twice in the past month and I'd love to know if any of you have had success with this (with respect to off-cycle openings). Thanks!