Does Progressive offer car insurance to drivers with only a learner's permit?

Yes, it is possible to get car insurance while holding only a learner's permit. Working toward a license with a permit is one of the standard reasons an unlicensed customer buys coverage, and some insurers let the policyholder designate a licensed primary driver. Note that some companies may be wary of insuring customers without a full license, and some states require at least one licensed driver to be listed on the policy.