Question: I would like to know when is a good time to start teaching your baby sign language. I heard they won't start signing back to you before 6-7 months so starting before 3 months might be pointless. Any thoughts on when you think would be a good time to start for your sake as well as your baby's?

Answer: 
Just do it as normal all the time.

They pick up everything all the time.

That is how children learn by seeing, hearing and experiencing things.
What if a baby is born deaf? Once parents learn their baby is profoundly deaf, sign language begins, presumably with a baby that can see. Try imagining (as a hearing person with ear plugs on in a very noisy environment) and attempt to listen to someone talking to you. If you can't hear them, you're deaf and relying on your eyes to see their lips move. Lip reading becomes automatic for a deaf baby and sign language a 'normal' skill learned no differently from learning to speak. A deaf baby immediately focuses their eyes, as all babies do, to the person in direct contact. Signing begins immediately. Sign language is the deaf's way of speaking until old enough to learn speech from professionals in deaf schools. Remember, as a deaf person, if you never heard a sound since birth then how do you know how to create sounds into speech since you're deaf from birth? I'm one of several siblings to an older brother born deaf. Mother, father and the rest of us have normal hearing.