Registering a SSL Certificate in C# .NET AWS Lambdas

I'm trying to connect to a SQL Server 2019 instance (happens to be in an EC2) from a C# .NET AWS lambda. I'm using a self-signed certificate to establish client trust with the SQL instance.

There doesn't seem to be a lot of documentation around how to register certificates in AWS. The documentation I can find is third party, and revolves around using OpenSSL's SSL_CERT_FILE variable to expose a lambda layer path for OpenSSL to interrogate as a root trust (https://dev.to/leading-edje/aws-lambda-layer-for-private-certificates-465j)

I've used the SSL_CERT_FILE approach in the past with success, but it doesn't seem that SQL is using OpenSSL for that trust connection.

What alternative approaches have folks used? Has anyone had success with actually registering certificates in an AWS Lambda? (instead of exposing it to specific SSL libraries, like SSL_CERT_FILE does)