That’s a great idea! While this is currently not possible, I’m sure others would agree that this is a nice feature to have.
You can submit this suggestion to the Idea exchange, under Platform ideas and improvements.
Don’t forget to search for it first, just in case someone already suggested it, so that you don’t end up creating a duplicate.
A workaround you can do is simply create a subdomain redirect to the organisation dashboard.
Note: this is not the same as Domain Claim —
Enterprise customers can now claim and verify an email domain for their Single Sign-On (SSO) setup, allowing for SSO enforcement. Make recognizes users with the claimed email domain and prompts them to use SSO. See our article on domain claim for information on setup and provisioning options.
Domain claim only redirects users signing in with your domain name to your SSO.