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: 
We incorporated basic signs with our children pretty much right after they started opening their eyes (i.e. around 1 month) and coupled it with words. We are not proficient in sign language, we limited ourselves to 'eat', 'drink', and 'more' and was done with a deliberate goal towards the long game and had demonstrable benefits for us.

Our kids are now 3 & 5 and are 3 year old will sometimes fall back on his sign language when he's extremely upset and that's where the benefits really show. Temper tantrums can make forming his thoughts into words all the more difficult, so having a few signs to help him say what he wants can be very helpful for him to convey his desires without words.

He even uses it at bedtime as his way to say, "I love you," and it is the cutest thing ever.

So to summarize, anytime is fine, but I will say there are benefits to be had. It probably won't prevent temper tantrums from occurring, but it will make them a little easier to handle.
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.