I think the minimum age really depends on the maturity of the child ... and the maturity of the parent ...
... Bob (Grateful Diver)
I completely agree, but this is not enough.
And with maturity comes knowledge and concerns, as there are risks associated to kids diving that are not linked to maturity.
Long term pressure exposure, and a few other, explained here:
Why I Do NOT Train Kids In Scuba Diving
Even if you limit the depth to 40ft like Padi does, it is far enough to generate some, even the most minor risks of little DCS, which impact on the future growth of the child bones you have no idea about.
But like many other sports, it's a decision liked to compromises.
I have an extremely mature kid, certified since 11y, from Padi JOW, and has about 30dives. If I dont really care whether or not an OW class is enough to make good adult divers, the JOW is far from enough to certify any kid, whether they'll dive some instructors or their parents.
I/we taught her much more, read many stories (best: diver down, where some stupid kids and adults makes some stupid decisions and die)
Now she's the one pushing me not to take any risks (which I don't, but she stopped me from diving with a patched wing once). She is one of the reasons I went to a certain form a training and diving approach.
Still if we dive together from time to time, she will not be able to dive without me or her mother before she also goes through more advance training.
But the link above, and the potential risk of minor DCS happening even in simple and easy rec training (added risk of drysuit diving learning curve) gets me very worried.
Even moving forward, the parents will hold the responsibility to have put their own child into this activity, which can remain dangerous, sometime more than American footbal, boxing or other !
A potential answer to the poll would be when the child stops growing (to limit the potential impact on bubbles in bones...) ... but then for some it's between 18 and 20 !
Very difficult to wait this long to enjoy a very cool family activity !