Dear Sir/Madam, good afternoon!
According to Article 119 and 12 (paragraph 5) of Law 5038/2023, after completing their studies, students can apply for this residence permit to look for highly qualified work for one year. Therefore, in this case, it is not necessary to attach a contract.
Please see also:

Post study work residence permit in Greece

It is very important to indicate how Article 119 of law 5038/2023 applies in this case.
Please provide clarification.