First Party Clients using Domain Level Connection via API

We are needing to have our existing first party clients become enabled for a connection that has been promoted to domain level. The idea is they will not be explicitly managed via enabled_clients. Instead, (1) We have first party clients already created, prior to creating a new connection for a customer.

(2) Upon create a connection for a new customer, we promote it to domain level immediately after creation.

(3) When attempting to login with the client, an error is returned stating the connection is disabled. If we manually enable the client for the connection in the dashboard after that, it works: but this is a manual process and not an option.

(4) We need this process to be automatic: Once the new connection is created and promoted to domain level, our first party clients should work for the customer.

(5) We are planning to accommodate both first and third party clients, but wish for first party clients to have access to domain level connections (no consent screens).

Is first party client access to domain level connections supported in Auth0 via promoting the connection, or must they always be enabled for the connection directly by updating the enabled clients property?