An egress-only internet gateway is for IPv6, not IPv4. A VPC endpoint (Gateway type) for S3 or DynamoDB does not provide general internet access. The only remaining possibility is that the subnet's route table has a default route (0.0.0.0/0) pointing to an internet gateway, but the instance is in a private subnet? Actually, if it's a private subnet, there is no direct IGW.
The most likely cause is an AWS managed NAT gateway? But the question says no NAT gateway. Another possibility: the instance has a public IP assigned? But it says no public IP. Let's re-evaluate: The stem says no public IP and no NAT gateway/instance.
Possibly the VPC has a transit gateway or VPN? The answer might be that the VPC has an internet gateway attached and the subnet's route table has a default route to that IGW, but that would mean the subnet is public. However, the instance is in a private subnet (no direct route to IGW). The only way to get outbound internet without NAT is via an AWS service like a VPC endpoint for S3 or DynamoDB, but that's not general internet.
The correct answer is likely: The instance is using an AWS managed NAT gateway (but the question says no NAT gateway). Hmm, maybe the instance has an Elastic IP? But no public IP. Let's think differently: Possibly the instance is behind a Network Load Balancer with internet-facing? No.
The correct answer is: The VPC has an internet gateway and the subnet's route table has a default route to a NAT device that is not a NAT gateway (e.g., an EC2 NAT instance), but the question says no NAT instance. I think the intended answer is that the subnet's route table has a default route to an internet gateway (making it a public subnet), but the question says private subnet. Actually, the explanation should indicate that the subnet is actually public, but the engineer mistakenly thinks it's private.
However, the answer options: Let's provide plausible options.