Looking at my cp12 notice, there are two dates. For example, mine gave 4 to 6 weeks after the notice date but there is also an additional date on the letter stating that they will proceed if no contact by me is made after the later date on the notice.
So, I would honestly assume, from what I researched, that the return can come by check or direct deposit and somewhere between 3 to 12 weeks.
The best way to see updates is by logging into your online account. You can see your transcripts, and cycle code there.
Hope this helps!
