As of January 2021, there is no possibility to automatically register the public IP address of the Elastic Network Interface (ENI) of a created EC2 instance under a particular DNS name (or some form of proposed "pattern") in Route 53 as an A/AAAA record.
Just like you said, you gonna have to trigger AWS API calls to do that by any means provided (CloudWatch Events, EventBridge Events or as part of any Infrastructure-as-Code deployment of your EC2 instances using CloudFormation, CDK, Terraform, etc).
Of course, if your domain is not administered under a Route 53 Public Hosted Zone, you have to take appropriate actions on behalf of your domain registrar in order to register the public IP address under any A/AAAA record.
与恶龙缠斗过久,自身亦成为恶龙;凝视深渊过久,深渊将回以凝视…