Authenticating git http requests against an external identity provider

We are using GitLab’s repository management as part of a larger system. We only access it through the API, by using admin credentials and the ‘sudo’ mode. The user accounts are handled with an external identity provider, but are mirrored in GitLab by matching the user-id’s.

We would like to be able to use the username and password for the external idp also for authenticating git operations (only http/s), namely push, pull and clone. Is there some obvious way this could be achieved without putting a proxy between GitLab and the git clients? If the idp supports LDAP connections would that work?