We must be using different forms of English, then, because they sound the same to me. “Thin” and “then” do not.
In US pronunciation, Then is ðɛn and Father is ˈfɑðɚ.
In UK (received), Then is ðɛn and Father is ˈfɑːðə(ɹ).
In Indian English, Then is ðɛn and Father is ˈfɑːd̪ə(r)