How can I say in English that students have passed all of their exams in the shortest period, that is, the first time exams were scheduled (only the first examination term was used)?
While I don't find the following particularly informal:
They passed all their exams on the first try
You could also go with one of the following if they better suit your tastes:
They passed all their exams the first time they were offered.
They passed all their exams during their earliest opportunities.
Or you could turn it around:
None of the students needed a second attempt at any of their exams.