Unless the Cultivation Path Ancestor takes action personally, fulfilling those three conditions concurrently is impossible.
Even if the Cultivation Path Ancestor does take action personally, there's no certainty those three conditions could be simultaneously met.
It is commonly known that after Pangu established the heavens and the earth, he fell and transformed into the world and all creatures. Afterwards, Hong Jun took control of the Heavenly Dao and became the Cultivation Path Ancestor, effectively inheriting Pangu's legacy.
But there is not necessarily a direct connection between the Cultivation Path Ancestor and Pangu.
Instead, the Three Purities are Pangu's biological sons, formed from Pangu's primordial spirit.
Saint Taiqing can be considered Pangu's legitimate eldest son, inherently possessing the strongest right to inherit the world after Pangu's creation.