API Gateway - HTTP & REST API without using Route 53 having a custom domain on Cloudflare

My requirement is simple statement. I have a domain registered with cloudflare, I want to host a subdomain on AWS Lambda with AWS API Gateway. I can't transfer / use Route 53 Name Servers.

I have created an API Gateway HTTP api with stages $default. I am able to access it with Invoke URL which is https://5obxxxx02.execute-api.ap-south-1.amazonaws.com. It shows the API as Not found which is alright as I have not added any API.

Now, I added a custom domain after adding a ACM certificate for my domain. And I got API Gateway domain name. i.e d-xxxxxxxofdk.execute-api.ap-south-1.amazonaws.com

If I try to access it on Browser It gives me following error.

The following error was encountered while trying to retrieve the URL: http://d-6qxxxxxxxk.execute-api.ap-south-1.amazonaws.com/

Connection to 65.2.00.1 failed.

The system returned: (111) Connection refused

The remote host or network may be down. Please try the request again.