Yes, with certain car insurance companies it’s possible to get a policy with only a learner's permit, but there's a catch. Typically, you will need to be able to get a driver's license within a short period of time, usually 30 to 45 days, to start a car insurance policy with most auto insurance providers.
In addition, the insurance company might require you to start the policy with a driver who has a valid license until you have your own license.
Your age may also be a factor in whether you can start your own auto insurance policy with just a learner’s permit. If you are under 18, many car insurance companies will require that you have a parent or guardian sign on the policy with you, since you are still a minor and a car insurance policy is a legal contract. Most states require someone 18 years old or older to sign the documents to make them binding. Also, most car insurance companies have underwriting restrictions saying that the named insured cannot be under the age of 18.
If you are a minor and your parents already have a policy, you should see if you can be added to their policy for coverage. This will not only be easier but can save you money; car insurance for young drivers is very expensive. Being placed on your parent’s policy is still costly, but it's usually more affordable than getting a policy of your own.