в кратчайшие сроки(If you do something as soon as possible, you do it as quickly as you can: We need the repairs done as soon as possible. CALDAlexander Demidov)
в предельно короткий срок(as soon/quickly/much/etc as possible phrase as soon, as quickly, as much etc as you can. Get as much information as possible. Hold your breath for as long as possible. MED Alexander Demidov)
в сжатые сроки(At the earliest opportunity. Call your mother as soon as possible–she's very worried about you. Farlex Dictionary of Idioms Alexander Demidov)