So, elements such as iron, gold, etc. are formed from different types of supernovas, whether it's type 1A or 2. My question is, is it possible that there are elements that are formed that we never received during the formation of Earth and that we are unaware of? Or have we discovered every non man-made element?
It's very likely, that we don't have discovered every non man-made element. For some elements there exist only very short-lived isotopes.
This paper mentions the detection of a curium ion in cosmic rays. The process which forms curium can also form elements beyond curium, hence it's likely that there exist short-lived isotopes of elements in nature, which have not yet been detected. Research in this field is going on.