Closer to 8 weeks for me.
I applied and paid for car pool stickers when I still had paper plates. Stickers came soon after metal plates arrived.
In the mean time I cheated on my 96 mile daily round trip. I carried the receipt for the stickers in case I got stopped, not legal but I’m a good talker. My thinking was what cop is going to give a second look at a Tesla in the car pool lane? My windows were tinted too.
Never had an issue.