It's much quicker than it used to be. Usually several days from when the developer releases the patch.
Patching today is so much more common and both Sony and Microsoft do a good job of getting patches through. Plus there aren't arbitrary limits on the number of patches as there were on X360 and PS3, which usually only limited a developer to 2 post-release patches for a full game, without needing to jump through hoops.
I was expecting a Day 1 patch though as is common for most games, and we didn't get that.