Which solution will meet these requirements?

Explanations:

Configuring an internet gateway allows internet access to the VPC, which contradicts the requirement of not using the internet to connect to the S3 bucket. Additionally, updating the S3 bucket policy to allow access from the internet gateway does not restrict access to the private subnet.

A VPN connection provides secure connectivity to a remote network but does not provide a direct way to access S3 from a private subnet without internet access. Additionally, VPN connections typically require internet access to establish the connection, which violates the requirement.

A NAT gateway is used to enable instances in a private subnet to initiate outbound traffic to the internet but does not provide direct access to S3 from a private subnet without using the internet. Therefore, this option does not meet the requirement.

Configuring a VPC endpoint for S3 allows the EC2 instances in the private subnet to access S3 without using the internet. This option meets all requirements as it enables secure, private access to S3 without exposing the data to the public internet.