Hiya, I think you are jumping the gun a bit and worrying about your village a bit early. If my maths is right, you have a three year old. They are still quite dependent at that point so it's hard to childcare swap at the moment, unless you are fairly close. When your child is older, you may find a friend of two in the school mums where you find your village.
Mine are 9 and 10, if I have someone's children, the kids all entertain each other and I provide snacks. It works for me because while I may be the responsible adult, there isn't a lot of parenting happening. This is pretty much how it has been since they are 6. For the easy kids, they will just slot in with our lives and I have no problem having them with us if I have appointments because I trust that they will behave. In return, we will do more fun adventurous stuff (camping, campfires, beach trips, day festivals) and my record for a child staying is three days. For the harder work kids, we tend to just stay at home and they are gone by 4pm because I don't trust them not to run off and I can't have them at the drop of a hat because I may already have something booked that I can't cancel.
I am a fortunate stay at home mum and I'm happy to have children whenever but I do keep a mental list of the hard work kids and the mums who expect it. There are some children who are always welcome and others that I need to mentally prepare for!
When my girls were younger, I helped a "friend" with her child about once a week because she was going through a divorce (I was too) and she apparently had no time and needed time during the day to do her divorce admin because she was too busy in the evening (she never said why). Her child broke my daughters' things and was vile but I put up with it because I thought my friend was struggling. I stopped once she announced that she had a boyfriend and they were going out three times a week (suddenly realised why she was too tired to manage her own divorce!). Another lady in our school whatsapp group always mentions that her daughter is lonely and would like a playdate ("but by the way could you have her next Thursday because I'll be at work and I forgot to book childcare in the school holidays"). I don't help her either.
For the easy kids, I am the village and as a very fortunate single stay at home parent parent. I divorced someone awful but wealthy and it is not in my interest to return to work, theatre being said, I have no siblings, my mum has Alzheimer's and doesn't know who I am and my dad's idea of childcare is a TV so it isn't all roses. I'm happy to be the drop off house for SOME families. My friends are mainly full time high level workers with busy jobs but with an ability to run their lives like grown ups and who have healthy boundaries.
If we boiled it down to time, I probably have their children more than they have mine because I can, but if the children are easy and the parents are happy to reciprocate, I really don't care. I absolutely respect how hard they work and until this country wakes up and reduces the cost of childcare, we haven't got a hope.
I know they will also help me by taking either the children or the dog if I need them to. Their needs are "my husband is out of the country and I have a meeting in London, can you have her overnight in two weeks' time" and my needs tend to be "someone may have broken something, can you take the other child right now while I pop to A&E" and because their kids and my kids are easy, the answer is rarely no.
I think you will find your village where you can all help each other. In the meantime, my advice would be to raise a low maintenance, independent, polite child who at least knows that when they are guests in people's houses and they wake up early, that they need to read a book! They get invited more places and more people are willing to babysit (also cakes and flowers help too!!) 😄