As long as you follow your child's leads, then you are not being pushy. It is pushy if you force this on your child, but it is not pushy if you follow up your child's interests and questions. I think some parents fail to see this distinction because their children are not interested, and so they assume that all children are not interested, which of course is not the case!
My daughter started showing an interest in written words when she was about 2 3/4, so we got her the jolly phonics books. I just put them on the bookshelf and let her bring them to me. At first, we just did the single letter sounds (Until she was over 3 1/2), but it was only ever a game - she would spot the letter sounds she knew out and about and would point them out and do the actions. I never told her she had to do reading or anything like that, just waited for her to bring the books to me.
She is 4.5 now, and is quite a good little reader. I still follow the same policy, I put the appropriate books on her bookshelf and wait for her to pick them up... Sometimes she goes months without reading, other times she wants to read three or four books a day. Its up to her. When she starts school in September, she will have a very solid foundation from which to work, and what's more, because she has driven all of this, she has a love for reading and I have not had to force it on her. I have only ever facilitated her desire to learn. To me, this is the best foundation I can give my child.
The key thing is to let your child drive it, and keep it fun!
HTH