The correct option is Provision a DynamoDB gateway VPC endpoint and update the private subnet route tables. This approach uses a gateway VPC endpoint so traffic to DynamoDB stays on the AWS network and no internet egress or NAT is required while operational effort is minimal.

A gateway endpoint integrates with your subnet route tables so EC2 instances can reach DynamoDB through the managed gateway within the VPC. You add routes that point to the gateway endpoint and DynamoDB traffic is kept on the AWS backbone. This satisfies the security requirement to avoid public endpoints and internet egress and it is simpler to operate than managing custom VPNs or NAT infrastructure.

Deploy an interface VPC endpoint for DynamoDB and attach the ENIs in each private subnet is incorrect because DynamoDB is accessed via gateway endpoints rather than interface endpoints with ENIs. Interface endpoints use PrivateLink and are appropriate for many services, but not for DynamoDB and S3.

Establish a private DynamoDB endpoint accessible through an AWS Site-to-Site VPN is incorrect since there is no separate customer VPN reachable private endpoint for DynamoDB. VPC endpoints are consumed inside the VPC so a Site-to-Site VPN does not provide a native DynamoDB target and it would add unnecessary complexity.

Build a software VPN directly between the private subnets and DynamoDB is incorrect because managed services like DynamoDB do not terminate customer VPN tunnels. A software VPN to a managed service endpoint is unsupported and would increase operational burden without solving the private connectivity requirement.

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