AWS - Lambda invocation from Message/Notif/Event with exponential retry and ~1 day delay support between retries

Question

When the lambda function receives message/notification/event, my requirement is to process it straightaway but it fails, push it to AWS infra so that it can be retried with backoff approach with support for ~1day delay before final retry is triggered.

I am able to do first job (invoke lambda and process) but in case of failure, I am struggling to find a solution as SQS only supports linear retry (can't rely on visibility timeout as it is also linear) and SNS limits max delay to 1h. Triggering AWS events is not an option as it means all the messages will be processed with different retry strategy.

I would like to point out that I don't want to write a cron myself as it means I will have to run the check myself and also run cron every minute(which even though is a small task is something I would like to avoid). Also, FIFO is not an option as system should scale to support > 1m events.