Can I show off a facedown card at a battlefield with the Show Off ability of Gutter Guardian?

You cannot. Facedown cards don’t have any referenceable characteristics from their front side.

The keyword “Hidden” only appears on the front side of the card; that’s the side with the cost, name, Might, and rules text among other traits. While a card is facedown, any information on its front side cannot be referenced by other cards and effects. Although a facedown card may be friendly to Gutter Guardian, it doesn’t have the appropriate characteristic to be shown off. Note that only the card from hand is revealed with Show Off. You don’t reveal the friendly objects on the board that you’re Showing Off, so you can’t reveal the facedown card even if you wanted to.

Riot's question and answer, word for word, from theCore Rules: Radiance Patch Notes (Effective October 16, 2026)·Oct 9, 2026·Core Rules 811.5.a, 129.4 (as numbered in October 2026)