Can I still be written up if I’m at work before the hours of operation?

It depends on what the company policies and procedures are.  If the policy is not to allow employees on site until their designated work time, then that's the rule and they can enforce it. 

Many employers have rules that prohibit employees from "clocking in early."  This is a fairly standard rule because employers do not want to be liable for unbudgeted overtime.  This is an even bigger issue now with health care reform because the number of hours you are on the clock will determine whether you are a full-time or part-time employee. 

Other employers have rules that prohibit employees from working "off the clock," because they don't want to have potential exposure for pay day law violations (now or later). 

And finally, some don't like other employees onsite before their shift distracting other employees.

If your employer's reasoning is in line with one of the three discussed above (or similar thought process), then they can impose and enforce the rule.  As long as their rules are not in violation of a law or discriminatory, then they have a right to enforce their rules via a write-up. 

If you do not have a written employment contract, you are an employee at will. An employee at will has, basically, no rights in or to his/her job, and may be written up--or otherwise disciplined, or suspended, demoted, transferred, have his/her hours or pay cut, or be fired--at any time, for any reason, even reasons which are unfair or incorrect. So in the absence of a contract, you could be written up. If you have a written contract, if any of its terms or provisions would help you, you could enforce them, including through the courts if necessary.