Perhaps in an existential sense, every child has the potential to become a gadol hador. But, as we are told about the coming of Moshiach, it tends to occur with ???? ????. What is meant by this is that the goal of parenting is to continue the Golden Chain of our mesorah from ??? ??? ???? ????? and to pass it on to our future generations. This ideal of the “gadol hador” is neither meaningful, nor is it possible.
It might be worthwhile to visit or revisit the instructions given by Rabi Yehuda Hanasi to his children prior to his passing (Kesubos 103b). Each was guided to maximize his own potential. Only one was instructed to continue the royalty that he had himself inherited. That is responsible parenting.
A fatal flaw in our chinuch system is the delusion that yeshivos can create gedolim. That’s why so many try to set ridiculous standards, with denying admissions, expelling talmidim for being a challenge, etc. Just peruse at the biographies of the roshei yeshivos of prior generations. Look at the pictures, and tell me if today’s white shirts are faring better than the average talmid of R’ Shimon Shkop.
It is no smarter for parents to live in such a fantasy than it is for yeshivos.
Another interesting observation about the OP is that it seems to suggest that the individual’s own bechirah is at best a secondary matter. How foolish! A child with the best of environments can still choose otherwise. Tefilloh makes a big difference, since we mortal humans have a minimum of real control.