Lambda function that poll events from SQS only the first day of the month

Question

I require a lambda function that only polls fifo SQS queue events on the first of each month. Can it be done?

For example, one function will add events to queue on first of the month only, and the second function will process queue in the same day. I want something similar to this: https://docs.aws.amazon.com/lambda/latest/dg/with-sqs.html

But there are some requirements. First, each message should be processed by a dedicated lambda invocation. The concurrency limit must be 1, and finally, the polling should be happening on the first day of month only with the rest of the month queue is empty.