How long does it take for Steam to re-fill product key stock?

With the recent steam sales, I bought a game that was -50% (GTA V).

When it finished downloading, I tried to launch it for the first time, but I had an error message saying they were out of stock for product keys on this item (I can copy-paste the message, but it's in french).

Has anyone ever encountered this ? How long does it normally take for them to replenish their stock ?

Solution 1:

Steam is only allowed to distribute the amount of keys they have being authorized to distribute from Rockstar due to this you got the out of stock for product keys on this item. No information online from Steam actually states how long it will take so the information from forums should be taken with a grain of salt:

Took Steam 3-5 days if I recall to send the first key

(Source)

I would say wait a two/three days and then consult support if it does not start working.