Younglings practice with training lightsabers, basically low-powered sabers with no cutting ability. These replicate the look and feel of a normal lightsaber but with next to no chance of accidentally cutting your fool head off if you make a mistake.
Sometime between the ages of 8-13ish, when a youngling is ready to become a padawan learner, they undertake a ritual known as "the Gathering" with an eye to constructing their own (real) lightsaber.
The Gathering was a rite of passage of the Jedi Order meant as a
lesson to teach the young Jedi to overcome their own personal fears or
failings to find a kyber crystal attuned to their Force presence on
the Crystal Caves of Ilum. Upon retrieving the crystal, a Jedi
initiate began the process of constructing his or her lightsaber,
under the guidance of Professor Huyang. Part of the training process
of a Jedi, it signified a youngling's readiness to be selected by a
Jedi Master and begin training as a Padawan learner.