In Satya Jatakam, Satyacharya wrote that there are 3 moments which can be taken as birth time.
1) Adhana lagna (The moment of conception)
2) Siro darshana lagna (When the head becomes visible)
3) Bhu patana lagna (When the body touches the earth or when baby completely leave the mother’s body)
He further professed that, the first two moments are hard to ascertain and hence, one should take the third one.
For caesarian operation we may also take the 3rd one (Bhupatana lagna).