If you are a writer, it is fun to join the local writers group. I did this when I moved back to England after more than twenty years abroad. I fit in as a writer with the group - and this is the important aspect of it - "feeling as though you fit in somewhere".
If there is a local Book Club, then this is a good way to express your thoughts and get to know other's thoughts, to slowly build connections.
If you are a walker, or have some hobby, then perhaps there are like minded people in your area, who would be happy to include you in their plans.
I also found that the local library had notices which helped me get to know who my neighbors were. I learned how very different we were. The local newspaper was a source of local information too.
I once submitted a poem to a competition the newspaper was having and, as it happened that week, I won! The journalist came to photograph me and I went onto the front page. People said "Oh I saw you this week in the ....and we started chatting" (and it was about what is dear to me, possibly even to them.....again it is all about how connections start to get made.)
About friendship though, it takes years to make a friend, I find.
I wish you every success in your new place. I'm not of a generation that has absolute faith in socializing through the network, though lots of people do and many with success.