You have to get that information from your dealer. They know the moment you sign the paperwork when your car will go into production.
Each dealership is allocated an amount of 328i, 335i, and XDrives each month, and they know the production dates for each. Your dealer should have provided you with an allocation number and a production date at the time you did your deal a month ago.
Call him, ask him for that information. What has happened to me in the past is that I wasn't given an allocation number and my shady dealer gave my car to someone else who was more persistent and ordered a more optioned and expensive version of my 328i. So I was pushed back two weeks simply because I didn't know the game.
This happened to my friend a few months ago in SoCal, so I told him to call other dealers in the area, see who had newer allocation numbers and move the deal. He did. And saved some money in the process too.
428i Gran Coupé | M-Sport Line | Premium | Technology | Dynamic Handling Package | HK | Driver Assistance
Mineral Grey Metallic | Coral Red Leather | Ash Grain | Park Assist | Adaptive M | Sirius | Rolex | Trophy Wife | Beach House