People who arrive early but have not started work are not working, and thus are not earning. If they are working, they have to be paid, whether it is before their scheduled time or after their scheduled time and whether or not the work is approved beforehand. If someone is working hours for which they are not approved, this may be a disciplinary issue, but they must still be paid for the work.
We have had issues with employees working at home, and according to government resources, if we have knowledge of that work, we are required to pay for it (whether or not the person asks for payment or not). We have had to stress to staff that when they work and are not paid, it is not they who are breaking the law but we, and we do not want to be put in that position.
Some states issue guidelines for employers which address issues like these. Check your state's government website. Your local library may be able to help you find those resources if you cannot.
Here is the relevant chapter from Especially for Texas Employers. The question you are asking appears to be covered by federal law, so this resource may be adequate for your purposes.