R.F.
Bless your heart!! It really is easy and it sounds like you all already have things in common - children the same age, working parents, probably the adults are about the same age.
Just ask them over for a simple dinner. It could be hot dogs, pizza, hamburgers. The food doesn't matter; it's the company. Make it early enough that the kids can play before bedtime and everybody can leave in time to put their children down at home.
If that goes well, consider an adults night out. Again, something easy -- maybe meet for drinks after the kids are in bed and left with a sitter. You said you love music. Perhaps a place where there's live music. Right now, outdoors would be a little difficult; but, when it's warmer, how about meeting at the park for a picnic? Remember, simple in the beginning.
These baby-steps will lead to friendships, generally. Most folks do love to be invited to something/anything. Then, they generally realize they need to reciprocate. But, even if they don't invite you, invite them to join you a couple of times. You'll be able to get a feel whether they want to pursue a friendship.
Don't worry about making things too complicated. I'm a great cook and one of my oldest friends wouldn't invite us over because she was intimidated by my skills. I finally told her I didn't care what she served me -- just invite me! We've been friends for over 19 years.
Just take the first step. Invite them. It'll get easier after that!
Good luck. You'll be great!
R.