Can a newborn foreign baby leave Indonesia before obtaining his KITAS?

Hi all,

I currently have a index 316 KITAS (student). I had a baby 7 weeks ago, and I finally got his official birth certificate, report of birth abroad, and his passport all settled. I went immediately to the immigration office, but because I was in the process switching schools, the immigration office is refusing to give my baby a index 317 KITAS (dependent under 18 born to foreign parent with KITAS).

He has 11 days left to obtain a KITAS before his 60 days from birth are up, then I'm fined each day for him being in the country and not having a KITAS.

I know with how slow things work here, so there is no way I can trust that the new sponsorship will be processed before then, let alone the time it takes for him to get approved after that.

Therefore, I've decided to just end my studies, leave Indonesia altogether and not return back.

Now I'm worried that they won't even allow us to leave at the airport. That they'll open my baby's brand  new passport and start questioning why he doesn't have a visa, and make us go back to the immigration to get him one before he can even have the ability to leave the country.

So my question is:
Do you know if a foreign baby born in Indonesia, with a brand new unstamped passport and no visa, is able to leave the country?

Thanks!