To trigger deployments using GitHub Actions running on EC2 server without internet access

Hi AWS, I am doing some deployments using GitHub Actions self-hosted runners which are installed on AWS EC2 server without internet access as those are organizations owned production servers and as a good practice they have blocked our internet access. Now the problem is in order to make a call with GitHub Actions you need to have an internet connection as it uses a REST API under the hood which is going to interact with GitHub. Is there any way around where I can do the deployment smoothly without worrying about the internet connectivity available on the server I am working or not as if we need to do a certain deployment after a lot of discussions we used to get the internet access temporarily and because of our current setup if we have to do some deployments at off hours it gets stuck because of the current issue we're experiencing.

After a long research, I explored something and I am attaching the links for your reference:

1. https://docs.github.com/en/enterprise-cloud@latest/organizations/keeping-your-organization-secure/managing-security-settings-for-your-organization/managing-allowed-ip-addresses-for-your-organization
2. https://docs.github.com/en/organizations/managing-organization-settings/disabling-or-limiting-github-actions-for-your-organization

But I am not sure if that's going to suffice my requirement if that's practically possible. Please suggest.