Forward GitLab Cloud logs to AWS

My team has a requirement to gather audit logs from gitlab and forward them to a central storage on AWS S3 bucket (or cloudwatch) where they are processed by a log management tool.
The only way I could find to do this is to create a lambda function in AWS that uses gitlab API to fetch the audit logs and store them in S3.
I was wondering if there is any better solution to this. Does gitlab enterprise (silver subscription) provide any out of the box way to forward audit logs to AWS?

Appreciate your help.