The only thing I "pushed" was swimming. However, dd didn't start early as she suffered with a lot of eczema when she was very little.
The one activity that I did start her on when she was a toddler (around 2 and a half) was dance. Not because I particularly wanted her to do it, but in response to the observation that she never stopped dancing! She is still doing it now more than ten years later - just lots more of it!
I did have ideas about activities that I thought would be good. Playing an instrument was one, karate was another. DD had no interest in either so I let those thoughts go. I allowed her to sign up for lots of things early on in primary school, as I thought it was a good opportunity to experiment. However, I didn't push any of them, and over time, they all petered out.
She discovered a new interest in drama when she went to secondary school - started off by signing up to a school club and then asked to do it outside school as well. However, it is still the dance that is her real passion. She loves it, and has benefited from it in so many different ways over the years. I could never have imagined all the positive experiences that have come out of it for her.
The thing is, I don't think you can force these things. Kids will have their own interests. It was evident that dd was going to be a dancer (as a hobby, not as a career!) from before she could even walk - no exaggeration! She had an instinctive physical response to music even as a tiny baby. No idea where she gets it from, none other dancers in the family!
The thing is, the vast majority of children who learned dance with her in the early years subsequently gave up and found other hobbies/pastimes instead. Only a very few who truly loved it kept going.
I guess what I'm saying is to keep an open mind and take your cues from your child. Expose them to lots of different possibilities but let your child take the lead and discover his/her own passions.