It was a long night giving birth on a live stream, but Twitch star Fandy , her hubby Bryan , and their brand-new baby still popped by TMZ ... spilling the tea on their totally unorthodox delivery .

The trio hit up "TMZ Live" Wednesday, with Harvey and Charles grilling them about saying goodbye to the concept of privacy ... but Bryan shrugged it off, saying it wasn’t a big deal for them since they just wanted to educate people -- especially men -- on how birth really works. Play video content

Bryan opened up even more, telling us it was an eye-opening experience for him too ... and he hoped sharing it could help others prepping for the whole birth process.

Catch the full clip ... Fandy even tackles the big question of why they did it in the first place, so listen to her re

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