How and When would domain name would publicly available on the internet ?

Couple other things to check:

1. Make sure the instance is in a public subnet (the route table associated with the subnet has a route to the internet gateway)
2. Make sure the Security Group assigned to the instance has inbound TCP port 443 and/or 80 from 0.0.0.0/0 allowed

DNS can take 72 hours to fully propagate (but usually it's a lot faster). Using Google Dig/nslookup etc check that your domain name resolves to the same IP address assigned to your instance.