Ideas on how I might go about adding a universal setting for all Gutenberg blocks?

Is it even possible to add a setting to existing and future blocks? Is there a block "model" file I could edit, one that is theme-specific?

I want to be able to add a data-attribute to the topmost HTML element of any block, and it needs to be selectable by the user (I can't just do a RegEx because I don't want to add the same attribute to each block.)