When do pilots engage the autopilot in airliners?
The minimum altitude for autopilot engagement is generally the acceleration height or around 400' AGL though this can vary between operators.  

The question of when the autopilot is actually engaged is a more complicated question and is subject to pilot preference.  Personally, I generally hand flew until the first level off or until climbing and accelerating through 10,000 MSL.  Others may turn it on as soon as allowed and most fall somewhere in the spectrum between the two.