Can I have a small wage if I establish a non-profit organization/company in Greece?

A non-profit is created and run by a board of directors. Although you would be on the board initially, you would have no absolute right to be on the board, and the board could choose to replace you with someone else. There is nothing special about being a founder of a non-profit.

A board member of a non-profit may be paid for their time, though often they are not.

Many non-profits have employees who are paid a salary, and you can be on the board and also be an employee.

This is all from a U.S.A. perspective but I expect it is the same for Greece.