It depends on where you are within your Group/Batch.
I was in Batch 2, and it took me about 4 weeks to get my shipping notification after confirming my address. For some of my friends in Group 3 & 4, it took 6-7 weeks after confirming their address. The batches are quite large, so if you're towards the back end of the batch, you'll experience a longer delay.
Be sure to post here when your Playdate arrives! You're gonna love it, well worth the wait.