As soon as is possible; at one's earliest convenience; at the earliest possible time.
Usage notes
This is not an idiom. It is a particularly common instance of the general construction: "as X as Y", where both X and Y have a large range of possibilities. X can be an adjectival, an adverbial, or a quantifier determiner (much, little, many, few) and Y can be a clause or an ellipsis of a clause. The full clause for which "possible" is an ellipsis depends on the preceding verb. "He left as soon as possible" is an ellipsis for "He left as soon as it was possible for him to leave." When Y is a noun ("He left as soon as John."), the ellipsis is still for a clause ("He left as soon as John left."). So if one was going to do something as soon as possible, then one would perform said action as soon as any impeding activity was no longer an obstacle.
Korean: 가능한 빨리(ganeunghan ppalli), 되도록 빨리(doedorok ppalli)
Kurdish:
Sorani: Lua error in Module:parameters at line 360: Parameter 1 should be a valid language or etymology language code; the value "ku" is not valid. See WT:LOL and WT:LOL/E.
The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.