At what point can I study philosophy in the Hawza of Najaf? Can I study it alongside my Muqadimat (introductory level studies), or is there a specific time for it?
Essential Islamic knowledge is which helps you knowing then teaching others the Islamic teachings. Arabic, Quran, Fiqh,, Hadeeth and Logic is to start with. Philosophy comes later after building a strong base of Islamic knowledge.
'Philosophy has many types including Islamic and non Islamic philosophy. You should not waste your time in non Islamic philosophy which does not guide you to Allah, nor help you guiding others to the teachings of Ahlul Bayt (AS).
Your teachers in Hawza should be able to assess your progress in your Islamic studies then guide you when you need to study philosophy.
Wassalam.