I made SO many efforts with local mums. Only one of those became a proper friendship. But while I was making the effort, there was a massive amount of socialising - weekends away in Uk and abroad, loads of parties, girls' nights out. It must have looked like we had the greatest social life, but I didn't really feel that connected to any of them in the end. That social life came from doing everything possible when DC were small. I volunteered at playgroup, church creche, after school and holiday clubs, school PTA. Looking back, I should have done less and relaxed more and would probably have found real friends more quickly.
Think of three things you genuinely love to do or are interested in - that you'd do anyway, even if you made no friends from it. Sports, dance or fitness, gardening or craft, choir, acting, book club or creative writing, political or environmental campaginging etc. Look for lively groups in your area and join a couple then relax. Don't try to 'make friends' for at least a year. Just turn up and enjoy doing what you are doing. But stay open to invitations. If there's an aspect of a project you or someone else needs help on, suggest chatting about it over a walk or a coffee. I found that was how good friendships started, away from the crowd.
Most of my closest friends are from a specific semi-pro hobby that is work related. I met them first online in a specialist forum, locally through a weekly group and also through work which overlaps with the hobby. Then some of them are friends of friends who became my own closest friends.
Apart from them, after eighteen months of fitness classes, we are starting to meet for coffees and drinks outside of class (could have been extra-slow due to Covid) and getting to know each other. I have discovered lots of lovely women who I would never have otherwise met. They may not be best-friend, soul mate material but we have a great coffee catch up after class and chat about our kids, holidays etc.