Custom SMS sender Lambda trigger

I am trying to send a verification message via SMS using a Custom SMS sender in AWS. I want to include a sender ID in the message. However, I am facing issues with the Custom SMS sender and the Lambda trigger is not getting invoked.

I followed the instructions in the following AWS documentation to set up a Lambda trigger for my Custom SMS sender.

https://docs.aws.amazon.com/cognito/latest/developerguide/user-pool-lambda-custom-sms-sender.html

I have double-checked my configurations as mentioned in the documentation, but unfortunately, I am still unable to trigger the Lambda function. I have configured the custom SMS trigger sources to be triggered by user signups in AWS Cognito. How can I resolve this issue and successfully send the verification message with the sender ID?