Yes. You can start work with your digital work pass in the SGWorkPass app. Download SGWorkPass app and set up your digital work pass if you have not done so. You may register or reset their Singpass, if needed.
Alternatively, the the notification letter is a temporary approval before you get your card. A valid notification letter allows you to start work and also enter or leave Singapore.
The notification letter has a validity period of 4 weeks, which will allow you enough time to receive your work pass card.