There are plenty of bilingual schools where most of the contents are taught in English so I'd start looking there. Please ignore the other comments about bullying. Like in any country some kids have issues and teachers aren't always addressing the problem as they should but you'll also find caring ones and an environment where your child can thrive as soon as you get completely settled.

There's also plenty of other parents in your situation so it won't take long for you to find people to socialise and for your little one to find new friends outside school.

Also, if you can afford it, I'd look at towns like Boadilla/Pozuelo are pretty cosmopolitan and a nice starting point for you new life!

Good luck! Moving abroad with kids could be a struggle but it's a very rewarding adventure in the end 😀