time, occasion
砌 centers on a specific point or juncture in time: an occasion, a moment, or a particular time when something happens.
砌 combines 石 (stone) with 切 (cut). The exact historical development is uncertain, but it may relate to a stone threshold or step, which can mark a point in time or occasion.
Picture a stone 石 threshold that you cut 切 to mark a special occasion. When you step over it, you know it's time for the event.
For サイ, imagine a sigh of relief when the occasion finally arrives: sigh -> サイ, and the stone threshold marks the moment.
time; age; chance; moment; occasion