AWS Parameters and Secrets Lambda Extension throwing BadRequestException

I have been trying to use the AWS Parameters and Secrets Lambda Extension to access parameters from the parameter store using this guide https://docs.aws.amazon.com/systems-manager/latest/userguide/ps-integration-lambda-extensions.html

The problem is that if I try to access the parameter store(which runs on http://localhost:2773) as soon as the lambda starts up then I get a 400 BadRequestException error from the parameter store with the message not ready to serve traffic, please wait

If I add a delay of 100ms before accessing the parameter store then it works fine and successfully fetches the parameters. The 100ms delay is a blocker for using it in any production environment.

Is there a way to use the extension without introducing any wait times for initialization?

Thanks