Is it easy to get my baby's passport for the first time? Which branch is the most child-friendly?

It actually depends on your location. If you are based in the metro, you can go to DFA Manila or to its satellite in SM Megamall in Mandaluyong. I've actually read some blogs about moms who have filed their babies' passports in SM Megamall. They say it is spacious enough, well ventilated and the staff including the guards are very friendly. ;)