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.
Unless he/she has a hearing impairment just to talk to them. Of course point at the things at the same time, to show what you mean ("You want water?" and point at the bottle) but don't replace talking with signing.

Believe me you'll understand their babbling and they will understand you like any other baby did in the past even without sign language attempts.

Anecdotal evidence: a friend of ours is doing this signing thing with her toddler boy. First of all it looks really odd, like why is she flailing hands when she can simply tell him what she wants? And second the boy is now quite behind with speech development because he can comfortably communicate with his parents using signing and has no need to develop a spoken language.

Trust me your baby will be just fine if you just speak to him/her. All the best.

**Updates based on the comments:**

1. I'd suspect that most parents don't know or use the official, true sign language when "signing" with their babies. The name is misleading, it should be called "baby-level hand gestures" as that's what it is. Calling what they do a "sign language" leads to a confusion like we have seen here and it is indeed demeaning to the official, proper sign languages.

In other words I'm *not* dismissing American Sign Language, British Sign Language, or any other sign language of any country.
2. That misunderstanding also led to some accusations of ableism in the comments. There was *zero* mention of any impairments in the OP's baby or their family, in other words the assumption is that they *are able* to learn to communicate verbally. If it wasn't the case it would certainly be pointed out in the original question. That makes me assume that the OP doesn't have a real need to sign with her baby and is only considering it because it's trendy in some circles.

This answer is obviously not relevant in a situation where the baby or the family *need* to use a *proper* sign language. However to my understanding this is not the OP's case.