Are those words interchangeable?

-sometimes they can be used interchangeable

The black car finished the race in the first place..

Siyah araba yarışı ilk/birinci sırada bitirdi.

-if it´s like an experience never done before...

I saw her for the first time

Onu ilk kez gördüm

(we cant use "birinci kez" here)

That s not a rule but for many times:

ilk = for the first time

birinci = first

İlkin = for the first time

Very clear! Thank you very much!