There are no policies specific to donning the hakama. It seems the timing varies depending on the dojo and instructor (Men typically start wearing hakama once they receive a dan rank (black belt). This was the case for me, too.)
At Shishin-Kai, the decision is left to the individual, so you could start wearing a hakama right from the start (except for Kids Class). All dan-holders (black belts) are expected to wear one.
However, the hakama covers up the ashi-sabaki (movement of the feet), which is the most important part of Aikido. Because of this, kyu-ranked members (white belts) in our dojo practice with the hems tucked up for visibility.
As a side note, according to Japanese customs, it was standard practice to wear hakama before Aikido became widespread.
However, Japan was experiencing postwar shortages of goods at the time when more people began to practice Aikido. Therefore, it was impossible to oblige all members to wear a hakama. Still, consensus was made that at least the dan-holders would wear a hakama. This consensus somehow turned into the custom, “only dan-holders can wear hakama.”*
*Reference: Hiroshi Tada 2018, “Aikido ni Ikiru,” Nippon Budokan, p63 [In Japanese only]
