Reference Material:

https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/AuroraMySQL.Managing.Performance.html
You can increase the maximum number of connections to your Aurora MySQL DB instance by scaling the instance up to a DB instance class with more memory, or by setting a larger value for the max_connections parameter in the DB parameter group for your instance, up to 16,000.
You must change a larger value for the max_connections parameter in the DB parameter group, not edit my.cnf, it is not physical server hosting MySQL.