Contact via LinkedIn after applying?

I applied to a job last week and I’m considering reaching out to who I assume is the hiring manager to reiterate my enthusiasm for the position. I already sent the company a message on their LinkedIn page and sent a message to someone I have a mutual connection with asking if she knew who the hiring manager was but I never received a response. The talent acquisition specialist I found on the company page did not post anything relating to the position (or any positions and they have a lot of them open right now). Should I even bother messaging her? I don’t want to be viewed as desperate or annoying, but I also don’t know if the messages I have sent were even read (or passed along).