I am aware it is possible for administrators to delete badges if needed. Is the reverse possible - can an admin grant badges if needed?
A situation where this could be relevant is that a badge was not awarded due to a bug.
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The only two badges we have tools for manual awarding are Not a Robot and Census. We cannot and would not award any other badge manually.
If there was a bug that prevented an award from going out, simply fixing the bug is the only solution. Badges are not awarded on the basis of "when it happens" like in video games - rather we run a query on a schedule that looks for all cases that are currently eligible to receive a given badge and haven't yet received it, and award them based on that query.
While SE staff won't directly award badges to users, sometimes they will intervene to make a badge be auto awarded, e.g. see this case. In that case there was a bug/oversight causing a badge to not be awarded, so the developer manually changed the condition of the specific user so the badge could be awarded.