Addressing a company/hiring manager in a listing with no company name?

So I found a really intriguing job listing that was posted by a staffing agency. Decent pay and a long-term contract with a probable extension, so I want to approach the cover letter pretty carefully.

The listing is detailed and thorough, but the name it's listed under is the staffing agency and absolutely no indication of hiring or supervisor names, the position's department or company name.

So how do I address the people who would be receiving the cover letter? Other than something like "Dear hiring manager," how would I address the department/company and make myself seem like I know who I'm talking to. Or is this type of listing common and I'm over-thinking it?

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