The very coinage of the epithet "Mahavatar" to Babaji is in itself erroneous, a gross fallacy. "Avatar" infers a reincarnation and Babaji has been ascribed as a Mahavatar by so-called Kriyayoga Capitalists who choose to encash on this erroneous concept.
Much hue and cry has been raised about Babaji. A simple fundamental yogic truth has been advertently made complex and distorted by so called Kriyayoga stalwarts who have used Babaji to suit each individual's palate.
Sri Shyamacharan Lahiree Mahasaya who has Himself declared He is "SWAYAM BHAGAVAN" before He marked His Advent as Jiva-Shyamacharan had commanded his Brahma-Shyamacharan state to arrive and impart initiation to Him, because on arrival as a mortal He will forget His Brahma Shyamacharan state, in accordance with the yogic discipline and the Guru-Shishya parampara tradition.
So Babaji manifestation is none other than the Brahma-Shyamacharan Lahiree manifestation Himself. So Jiva Shyamacharan was imparted iniitation by Brahma Shyamacharan in the supernal form of Babaji. This proves that even when God marks His Advent as a mortal He will make it imperative for Him to abide by His own discipline.
True soul-seekers can be further enlightened on the Babaji concept through Mahamahopadhyaya Yogacharya Dr. Ashoke Kumar Chatterjee's two books which forms part of His triology on Sri Shyamacharan Lahiree Mahasaya i.e., "Purana Purusha Yogiraj Sri Shyamacharan Lahiree" and "Who is this Shamachurn"