Connecting to SQL Server at LightSail with SSMS

Hi - Have you checked the Lightsail Instance Firewall and Ports that are allowed? You will likely need to allow traffic inbound to your Lightsail instance on the ports that are required by SSMS. Please also remember that you would need to allow traffic from your specific public IP only so as to protect your instance. Please see: https://lightsail.aws.amazon.com/ls/docs/en_us/articles/understanding-firewall-and-port-mappings-in-amazon-lightsail

Yes, ping will need ICMP to be opened. Having said that, what about the firewall within Windows itself? Have you checked that?