Follow up for IT position on LinkedIn?

I submitted my resume today for an IT position at a major retailer that I'd really like to work for. The corporate IT recruiter's name was at the bottom of the listing, so I found him on LinkedIn. Not knowing the format of their email addresses (ie - jsmith@company.com, john.smith@company.com, john_smith@company.com), this would be the easiest way to reach out to him electronically.

I know it's early, but I would love to shoot him a message on LinkedIn to introduce myself and make sure my name stands out when he sees my resume.

What is really the soonest I should do this? I believe the position was listed for the first time today.

Relevant details: I have an interview with another company tomorrow (very local) and I'm in communication with a third recruiter to discuss a possible position 30 miles from my home. This retailer would also be maybe 30 miles away, but I'm more excited to pursue this opportunity than I am about the other two. I definitely want to express my preference for his position over these other two, but I also obviously don't want to come off as annoying or desperate.