Evidence of authority rather than evidence of headcount. Signed budgets, policies the person set, decisions taken without approval from above, and a clear account of who performs the routine work of the function instead.
Show the decisions, then show who does the rest
A petition claiming managerial or executive capacity for someone who supervises nobody is not doomed, but it carries an extra burden. The route through is function management: the person manages an essential function of the organisation, operates at a senior level within it, and exercises discretion over its day-to-day operations. Two things have to be visible.
First, the authority itself, which is proved by documents that already exist if the authority is real. A capital-expenditure approval carrying the person's signature is worth more than a paragraph asserting seniority. Second, and more often forgotten, the routine work has to go somewhere.
Hypothetical example: a reliability lead near Saint-Joachim-de-Shefford is put forward as the director of a U.S. function, and the petition never says who will take over the preventive maintenance and breakdown work that fills her current week. An officer reading that file concludes the transferee will keep doing it.
Naming the technicians, contractors or shared-services team who absorb the hands-on work is what turns the claim into a description an officer can accept.