User Access Token & Project Access Token Unavailable in FIPS Mode - Alternatives?

I need access to the GitLab API when it is deployed on a k8s platform with FIPS enabled. When GitLab is deployed on a FIPS enabled environment, User Access Tokens and Project Access Tokens become unavailable for security.

To make matters more complicated, my environment is behind an SSO authentication with 2FA.

What is the recommended way to authenticate GitLab API requests if Project and Personal Access Tokens are not allowed?

GitLab Version 15.5.0