Call of Duty Modern Warfare II has been pushing an Open Beta period for the game since it was announced and thanks to an Amazon preorder listing, we may have a date for that beta. A listing for the Xbox Series X version of the game had a beta start date of August 15th in the details when it was first published.
This is of course just a leak and may not be accurate to the correct date or factor in delays and changes before the listed date. It is also worth noting that this listing was just for Xbox and while it would be safe to assume all Xbox versions would get the same beta start date, it could vary between platforms like PlayStation and PC.
The game is set to release worldwide on October 28th for all modern systems (including the PS4 and Xbox One). The "Vault Edition” of the game also features early access to the open beta with no details on how early that access will be. You can currently preorder the game on all platforms and this year’s PC release will also be on Steam.