In the 23rd century, it was displayed that Zefram Cochrane didn't know about universal translator. That's why he was unfamiliar with and asked about its working principle to Kirk (Star Trek: The Original Series). It means, he never encountered universal translator in 21st century when he was on Earth.
Data banks of USS Defiant revealed in mirror universe that Hoshi Sato invented universal translator in the prime universe (Star Trek: Enterprise). At the time of first contact, she wasn't even born.
Both points say that Vulcans (the only interstellar party) didn't have universal translator technology at the time of the first contact. When it comes to non-universal species/language specific translator, its possibility was null because that was the first contact.
How did humans and vulcans really communicate during the first contact?