1. The verb "быть" (to be) is not a transitive verb! And "мужчина" is not an object! "To be" (both in English and in Russian) is a copula verb. And what comes after "to be" is grammatically a predicate.
2. The present tense of "быть" is rarely used in modern Russian. But if you decide to use it, it should be "есть", not "быть". "Быть" is infinitive (to be), "есть" is its present tense (am/is/are). So, not "я быть мужчина", but "я есть мужчина". But in 99% of cases you do not need this form.
3. In past and future there is a tricky thing with "to be" in Russian. You can keep the predicate in nominative:
"Я был мужчина", "Я буду мужчина".
But it is more natural to put it in instrumental:
"Я был мужчиной", "Я буду мужчиной".
This only works in past and future (not in present)! It is hard to explain why, but you may think of it as if you were describing a role:
"I played a role of a man", "I will play a role of a man". When describing a role, we use instrumental:
"Он работает врачом" - "He works as a doctor".