use amazon connect to set a specific date (April 12, 2022) to receive calls

You would need to invoke a lambda function (that checks the required date) in your contact flow.

https://docs.aws.amazon.com/connect/latest/adminguide/connect-lambda-functions.html

I think that you could use this https://github.com/aws-samples/amazon-honeycode-connect-integration-sample/tree/main/docs and change it just a bit to play with the date that you want your Contact Center to be available and not.

Hope this help.