Seemed like the only real entry point for those kinds of roles is to toss the resume into the pile in the automated system and cross your fingers.
A recruiter friend of mine (from a different company, in a different industry) advised me not to submit a cover letter. He seemed to perceive them as more of an annoyance than anything.
Anyway, never got a call back, which I don't take personally - I know there are probably hundreds of applications and that getting a call is probably at least 50% luck. I also know that the market is flooded now, and I have a good job already, so it's hard to get too bent out of shape.
In hindsight I wonder if a cover letter would have helped my app stand out. But either way, it's frustrating seeing a posting that looks like a great fit and feeling like the odds are so slim for even getting to talk to someone and actually having a chance of making a good impression.