Your documents do not need to be filed with the state while you are living. The required signatures make your documents legally binding in your state.
Once signed, we suggest you keep the documents somewhere safe. It's also a good idea to let the people you've named (And maybe some other trusted individuals) know that you have an Estate Plan and where it's located.
Your Executor / Successor Trustee will eventually file your Estate Plan with the local government once you've passed.