How to trigger a Lambda function at specific time set by a user in AWS?

Question

At a high level, I'm working on a "schedule" feature in an app where a user can set a time for something and get a reminder notification sent to them at that time. I need this notification to go out when it hits the proper minute of that timestamp (ex: 10:52).

I was thinking of creating a cloudwatch event to handle this, but the issue is this does not scale well as more users use the app and create schedules. I was thinking of setting up a trigger on dynabmoDB streams and TTL so that a lambda gets executed when something gets deleted from the TTL, but that can take up to 48 hours, and I need it accurate down to the minute.

Keeping cost and performance in mind, what are my options here?