I am just happy you are able to move! I am an avoider - but with my personality - I would bake some fresh cookies and pop over and introduce myself (with my child). As the conversation goes - I would do my best to get up the nerve to gently mention the noise.
I kinda think we are the loud neighbors here - we aren't crazy loud or anything - but the houses on both sides are never outside. I try to keep things down and as it gets later, I turn the volume down. If we have a very large party, I hand deliver invitations to my neighbors and at the bottom I give my cell phone and ask them to please call if things are too loud, someone parks in their drive, or for any reason and we will make it right immediately.
So far, so good.
I don't envy you and if I had a problem with a neighbor it would stress me out so bad.