At the earliest; indicating that even in the best-case scenario something will happen no sooner than the stated time.
その書類は早くても明日の午後にならないと届かない。
That document won't arrive until at the earliest tomorrow afternoon.
早くても来週まで返事はできません。
I can't reply until at the earliest next week.
引っ越しは早くても月末になる見込みです。
The move is expected to be at the earliest at the end of the month.