Hai teman! I think "Saya ayah." can fit perfectly fine in colloquial speech, so it could fit well here also. For example, "seorang" is also not required in Indonesian films, as "Merah Putih" trilogy, set during the Indonesian Independence Revolution, where an Indonesian character (the actor Lukman Sardi) says a Dutch officer (Rudy Wowor), "Saya guru, dia petani!", that can mean "I am a teacher, he is a farmer!", in English.
I hope it helps.
Selamat belajar! :)