The ability to copy actions is present at birth
Infants have the capacity to mirror actions from birth. With a little bit a patience you can usually get a newborn infant to imitate you if you stick out your tongue.
In this first video clip you see Will (7 days) watching my mouth movements with great attention, and then eventually putting out his own tongue in response.
Mirroring games are a great way to engage a very cautious infant
Mirroring can be a very powerful way of engaging a very cautious infant. The trick is to not move in too close, and copy the actions the infant is making, and then to wait patiently for the infant to respond.
This next video clip shows an interaction between Wii (9 months) and me playing a mirroring game. The video nicely illustrates some of the important aspects of engaging an infant in a mirroring game.