I see this little mistake in push hands players all the time. Even experienced ones.
It’s easy to fix. It help you win and much more importantly it will speed up your internal development.
The simple mistake I notice the most during push hands, is that usually one (or both) players don’t start playing until contact is made.
When I am practicing/playing push hands, I don’t wait until I meet the other player to start playing.
1) Sensitivity: Learn to feel your opponent from a distance.
As I come up to the other player I am feeling for his center, where his structural breaks are and where he is holding tension. Find his root before you make contact. Build your sensitivity until you can know your opponent before they have the opportunity to know you.