Sledgehammer Games have confirmed that the player progression level cap for the Private Beta is Level 20. The level cap may increase throughout the beta period, but at the start on August 25, 20 is the highest level players can reach.
Alongside this, Divisions in Call of Duty: WWII also have their own progression system. The level cap in the beta is level 4, and this will not be increased in the beta. The highest level a division can reach is level 5.