Is it a sin to drive without your driver’s license? Whether it be within your control or not?

No. Emphatically NO! Do not confuse statutory law of princes with ecclesiastical, natural, or divine law. Too many do today. They think that whatever is legal is moral and ethical and whatever is illegal is immoral and unethical as though civil law is natural and divine law.

This would seem to fall under the category of "purely penal laws", meaning that they do not have a moral coloration, but if you are apprehended for doing so, you are morally bound to accept the civil penalty (fine or even jail time).  For instance, in many places, posted speed limits are routinely disregarded (such as on interstate stretches in urban areas), and nobody is ever pulled over for exceeding them by a few miles, but the law nevertheless exists, and if you were pulled over, the officer would be legally empowered to give you a citation.

Unless it were some sort of emergency, though, such as having to take a gravely ill or injured family member to a doctor or hospital in an emergency, it would be highly imprudent to drive without a valid license.

ElwinRansom1970 is correct in that civil law is not the equivalent of ecclesiastical, natural, or divine law.  On the other hand, a society may have legitimate reasons for certain of its civil laws, such as determining if someone is competent to drive without potentially causing harm to others.

The issue would depend on why one would be driving without a license, and I'm assuming the question is about someone driving without having a valid license at all, not because they forgot to have it on their person.

In most places anyone over a defined age can receive a drivers license by passing a written and driving exam and having their eyes checked.  Why would one want to risk the consequences of not having a license?  As FarmerWife said, if there were a particular emergency situation, like someone needs a ride to the hospital, that may be different.

Moral questions such as this are best asked of a priest and there is no where near enough information provided for even a speculative reply  For a couple of "for instance's" ...
If you lost or can't get a license because you can't pass the eye test you may be putting others in danger by driving without being able to see well enough, which could be a moral issue (i.e. the 5th commandment).  If you lost your license because you haven't been paying required child support (IMHO dumb for a court to take a license away for this, one may need to drive to get to work to have funds to pay support) it might be more of a "grey area" in terms of sin, but only a priest could give a legitimate answer.

Are you also driving without insurance? If so, when you are involved in an accident, you must be prepared to pay a great deal of money. To do otherwise (as in hit and run) would be immoral.

No moral objection exists to obeying the law which says you need a driver's license to drive. The intent of this law is to protect.

See this:
Then he saith to them: Render therefore to Caesar the things that are Caesar's; and to God, the things that are God's  [Matthew 22:21]

FYI, the only US state that does not require auto insurance is New Hampshire, but you must have a net worth of a certain amount to get a waiver.