Reaching out to department head prior to applying.

Hello all,

This isn't necessarily about a recruiter but I feel like this is a good place to ask.

There is a job posted yesterday on LinkedIn at a company I'd love to join and I feel like it would be a good fit for me. Upon looking into it a bit further I found that the Sr Manager I would be reporting to shared it and added the caption "Feel free to reach out if you have any questions".

In your opinions what would be a good way of approaching this? I'm likely over thinking this but I don't want to blow it, should I send a connection request first and then message them? What's the right mix of questions while also introducing myself and my background?

Any thoughts would be appreciated.