For instruction on a public road, the answer is effectively always yes. The learner permit is the legal instrument that makes it lawful for an unlicensed person to operate a vehicle in traffic, and no reputable driving school will take you out without one. Where it gets interesting is what you can do before the permit arrives.
Getting the Permit Usually Means Passing a Test First
In most states the knowledge test comes before the permit, not after. You study the handbook, pass a written or computerized exam on traffic law and signs, pass a vision screening, produce identity and residency documents, and the permit is issued.
This ordering surprises people who assume they will learn the rules during lessons. The theory generally has to be in place before any on-road instruction begins.
A number of states also require driver education to be completed, or at least started, before the permit is issued for younger applicants. Getting this sequence wrong costs weeks.
What You Can Legally Do Without One
Classroom and online driver education is open to you. In many states this is exactly where you should start, since it prepares you for the knowledge test and may be a prerequisite for the permit.
Practice on genuinely private property generally sits outside the traffic code, which is why some people learn clutch control and basic steering on private land first. Genuinely private is the operative phrase. Shopping center parking areas are usually open to public traffic and typically do not qualify.
Driving simulators, offered by some schools, involve no public road and no permit.
Once You Have It, Conditions Apply Immediately
A permit is not an unrestricted license. Expect requirements about who may supervise you, including their age and how long they have been licensed, plus restrictions on hours, passengers, and sometimes highways. Corrective lens conditions apply from the first minute.
Do Not Guess
Permit ages, prerequisites, holding periods, and supervision rules differ substantially between states and get amended regularly. Check the current requirements where you live before booking anything, and see how to prepare for a first lesson once you have the permit in hand.