I don't know if its a "good chance" that they filed for a permit within days of an order.
It depends on where you are. In Los Angeles, I had:
(1) an onsite inspection by Tesla to confirm the layout. I now know that this was because the city of LA and LADWP require very detailed plans. Its possible other cities do not. Some posters on here said they never had an on-site inspection by Tesla.
(2) an onsite inspection by the utility. This is probably partially due to the size of my system (16.32 plus 3 powerwalls) but may be required depending on the utility.
(3) Tesla draws up detailed plans. Mine are about five pages of very technical electrical outlines, etc.
(4) In LA it is taking weeks to get those plans approved. Not surprising to me, especially with covid.
It was a week or so between each step.