I wish I had done this when I first moved into our neighborhood.... Take Jr out for a walk. Go consistently and at different times during the day. You may not see folks out from your home, but if you walk around a few blocks, you may start to see people. If you get a hello and a wave, introduce yourself. Saying "I'm C. and we just moved in a few months ago. How long have you lived here?" And the conversation usually flows from there.
People love to be asked questions. Since you are new to the area, you can ask all kinds of things - hubbie and I want to go out to eat this weekend, where do you recommend? We may see XYZ movie, have you seen it?
Smile (it always makes people feel at ease with you if you have a warm smile), say hi. Approach them as if they are already your friend, and assume they are unless you start to get vibes otherwise. Always be kind and have positive things to say about others. If you are talking ill about someone else, people will assume you are talking ill about them too.
I'd volunteer at the school - maybe the PTO or something, or volunteer for the classroom parties or to help the teacher.
I'm also an introvert and I would constantly wonder what people thought of me after I met them (and still do, to an extent) -- did they like me, did they want to talk to me again? I exhausted myself. I finally told myself that I would assume they were my friend until I started getting vibes otherwise. But I also knew that if I started to feel they weren't receptive to me, I'd let them be.
I'm sure you are a nice person and expect that some of your efforts will be wasted on people who aren't interested in a new friend, but you also may meet a few folks who you really connect with.
Good luck! I feel ya!