Yes, you can set up a company without having a work permit. It all depends on the scope of work of the company and what kind of company you plan to use.
How can I work in Greece as a shareholder of a company?
I recently learned that although I cannot work for other employers as a Golden Visa holder, I could set up a Greek company as a shareholder. What are the specific requirements in this option? What is the scope of work I can do without breaking the law? How involved can I be in this business?
By being shareholder you can control your company's business activities. It's legal and you are not breaking the law.
As a holder of the resident permit title, the property investor does not have access to any type of employment. However, according to the law, employment does not include the exercise of economic activity in the capacity of a shareholder, a chief executive officer or a board member in an existing company. Of course, as shareholder you could take the related dividends but you could also exercise the economic activity through the position of board member or chief executive officer asking the management of the company and be involved in the business.