By utilizing the ping test suggested by @jarmod and @Naresh, I was able to establish that the instance was unable to ping ec2.us-east-2.amazonaws.com.

The problem was that the EC2 Launch Template was not set to auto-assign a public IP address.

The 'auto-assign public IP' EC2 Launch Template option is located in: Network settings : Advanced network configuration : Auto-assign public IP

To enable EC2 user data to associate an Elastic IP address, set the 'Auto-assign public IP' option to: Enable