This resource and doing it in a specific flow actually worked for me. Here are the steps for anyone trying to figure out the same.
System Preferences -> User & Groups -> Select the Account on the left -> Click on the account picture on the right -> Now create a new Memoji or select an existing one you have already created. -> Adjust Zoom, Pose and Style -> Click Save. -> Lock the screen and see for yourself If the Memoji is animated.
Note: If you see a square border around your Memoji preview in the bottom left, you probably have to start over.
Memoji not animated on MacBook Air (2020)… - Apple Community