How long does it take for a piercing to close just after getting a piercing?

a few days or just overnight

it actually really depends on the piercing.

A lip or tongue piercing will begin to close almost immediately if it was pierced very recently(within a month-ish of being pierced) However everyone is different but the mouth is known to be the quickest healing of the human body.

Ear lobes Vs ear cartilage piercing will differ as well. A lobe will heal faster than cartilage because cartilage takes longer to develop.

So it really depends on your body type and what type of piercing.