You can try with a global policy. Big companies such as Allianz or Cigna have policies that can cover you worldwide except US, they can cover life conditions under some circumstances. The only problem is expect to pay not less than USD 5000 a year
usually as an Italian parent having a kid in Thailand you go and register your son to your origin Italian municipality through the Italian Embassy in Bangkok. If you don't have a municipality in Italy, registration will be picked up straight by the Embassy. Either ways at this point for Italian government you automatically are the father of the child already. There is no other way for a kid to have an Italian passport, no other.