DS is 5 and now and at now life feels very different to when he was 2 and I felt like you.
I remember trying a baby football session, dh is football obsessed and would adore DS to play, we did one session and it was awful and a just cried all the way home.
We did tumble tots from 6 months to 2.5 years and by the time we finished as DS was going to preschool I felt like I was the only one whose child wouldn't listen and cooperate and I dragged him out kicking and screaming , I often cried on the way home from then too.
Swimming, he loved it but it got to a stage that he couldn't follow the same instructions as the other children. It was disappointing but we did persevere and the teacher who'd know DS from a baby was fine with him doing his own thing.
All of this together with the loneliness, upset, anxiety over having a non verbal child and watching how far behind he is next to their peers. It changed me as a person and I'll never be the same. DS is will be an only child.
I too found myself at soft play, parks, informal playgroups. I went to an ASD playgroup run by the local children's centre which was small and welcoming with no judgement. DS started at preschool and after a term or so loved going.
Fast forward to now, DS doesn't have a diagnosis and goes to a mainstream school with a speech and language resource. He's thriving at school and has made some lovely friends.
He is the complete opposite of the child that I cried with as I walked home feeling so lonely. Not only is he talking but we still swim and he follows instructions and joins in, we've started football again and he loves it and follows instructions. I'd have never believed it 2.5/3 years ago this is where we'd be. I don't know whether he'll get a diagnosis, we've been on the waiting list for 2.5 years and he's changed so much, life is so much more settled and enjoyable.
Don't try and put too much pressure on the both of you, do things that you know he'll enjoy which by default you'll enjoy. It's easy for me to dish out advice as I don't listen to myself but I spent a lot of time worrying about DS, to the detriment of my mental health, and I worry now, ironically, that I missed out on so much of his toddlerhood being sad.