What strength can accurately be attributed to the force of the throw?

Well for example if you're throwing a ball The force that moves the ball "up"

must overcome (be larger than) the downward force of the ball's weight.

Once the upward "force of the throw" overcomes the weight, it must then accelerate the ball upward, in order to give an initial upward speed.

Newton's formula: Fnet = ma

indicates that the acceleration (a) will equal the * excess upward force * {once the weight force is cancelled} divided by the ball's mass.

so in summary:

Fnet in Newtons will be the child's UPward force minus the ball's weight.