I won't believe that until I can make sure it’s the truth.
I won't believe that until I can verify it.
Norikoさんの英文は、次のように言うと良いですよ。
ーI won't believe that until I can make sure it’s the truth.
私なら次のように言うと思います。
ーI won't believe that until I can verify it.
「自分で事実を確かめるまでそれを信じないだろう」
to verify で「事実を確かめる」
ご参考まで!