In general, it takes less than a second for our system to generate a short link. Much less than a second.
It may take a little extra time depending on where you are in the world and the strength of your internet connection, but even so, it's generally in the tens of milliseconds.
The short link is active as soon as it's created, so there's no additional delay after you shorten the link. This is the case with QR Codes and buttons on your Link-in-bio page, too — they're also ready to be shared right away!