AWS Lambda access public network timeout
AWS Lambda cannot be placed in the public subnet. Lambda itself does not have NAT capabilities and cannot obtain public IP addresses.
So Lambda must be placed in private subnet. And configure NAT Gateway for it and add route.
Please refer to:
Give internet access to a Lambda function in a VPC | AWS re:Post (repost.aws)
amazon web services - Placing an AWS Lambda in a public subnet - DevOps Stack Exchange
Next check the security group.
AWS Lambda reports timeout when accessing secret manager
Add VPC Endpoint: