A set phrase used to express urgency or a request for prompt action. Often used in business or polite requests.
Please reply as soon as possible.
I'll finish it as soon as possible.
至急 is a more formal, urgent business term meaning 'immediately', while できるだけ早く is a softer request meaning 'as soon as possible'.
Standard kanji-kana mixed spelling; the most common written form.
Full kanji spelling; less common but still seen, especially in formal writing.
A phrase composed of できるだけ (as much as possible) + 早く (early/quickly). The expression is transparent and modern.