What I usually do is creating a bastion host (ec2) with SSH connection only, and then stablish a connection through this ec2. In my opinion this is way more flexible and easier than managing it through lambda functions - and also can be done automatically using serverless. The only thing you’ll have to do is connecting to the bastion host and running your script - or even create a script that does it all after the serverless deploy is successful, thus making your aurora db setup happen soon after it’s deployed.
I’m really curious if there’s a better way than automating this process, because I am using serverless less than a year, so this possibility is totally plausible.