Do I hear some personal frustration sipping through, BCP?
In my company we have a simple rule about engaging the autopilot on the A320: not before 100ft and only after 5 seconds after liftoff.
The rest is pilots discretion.
Think of a good reason to fly manually and fly manually; if you think you have a good argument to fly automatically, engage the a/p.
IMHO there is no standard rule about where to engage the a/p; it is situation-dependent. If the trainings captain has a good argument why to wait with the a/p, you could listen. Only stating "you're an aviator" is not a good enough reason for me.
Factors in deciding whether to engage earlier or not could be: weather (maybe you want to climb faster than is programmed), delay (speed up earlier than programmed), difficulty of departure (to keep an eye on tracking), noise abatement (a/p can or cannot follow the SID more exact than you depending on type of a/c) etc etc.
As an example of engaging earlier I take a Moscow-departure, where the PNF is busy changing frequencies, and you as PF can set the FCU, instead of, when flying manually, all the work to be done by the PNF.
An example of engaging later could be a regional airport with a lot of buildups in the departure path, and a very low amount of traffic.
I think the comment of your 3rd captain makes most sense of all: if you wanna be a captain, you'd better have an opinion!
P77