Here’s an intriguing article (unfortunately, it requires a subscription) promoting the ‘GPP’ – gender proportionality principle – that any given level in an organization should shoot for a gender balance that mirrors that of the level right below it. It also reports that gender disparities are most pronounced in levels of promotion, not in hiring:
Chilazi, Siri, Iris Bohnet, and Oliver Hauser. “Achieving Gender Balance at All Levels of Your Company.” Harvard Business Review. 11/30/2021.