Welcome to the world of Tesla customer service! The most odd thing is, the only way to find out is to check the app. There's a few stories of folks getting a call out of the blue that their car was ready for pick up despite checking their app "a few weeks ago" and it was months away.
Having said that, car delivery dates in general right now are all over the map for most manufacturers given the chip shortage. The difference is you talk to a live person who pretty much does what the app is going, guesses at when the car will be there.