Hello, David and Gustavo, appreciate on your attending my problem.
1. The source of above paragraph is unknown, which is among the problems of regular test for high school students made up by our Education Office.
2. When a friend of my mine asked me if we could leave out the above 'being' in the original sentence, I googled quite long time and found hundreds of thousand of results which were searched with the terms - "before given the chance/opportunity" - including following sentences, somewhat reliable ones;
1) I did not know how to be a “good” teacher before given the opportunity; I did not know how to be a cogent speaker before being asked to unfurl my life story on a global stage. And that made me realize that no one knows how to do it before actually doing it.
2) ... speed with which all ideas vanish and fall into oblivion before given the chance of maturing and ageing properly in our era of thoughts and things calculated, ...
3. in addition, the concerning explanation of Practical English Usage occurred to me;
p. 499, 5. ‘leaving words out’
However, after if, when, while, until, once, unless and (al)though, a pronoun subject and the verb be can often be dropped, especially in common fixed expressions like if necessary.
1) I’ll pay for you if necessary. (= ... if it is necessary.)
2) If in doubt wait and see. (= If you are in doubt...)
3) When in Rome, do as the Romans do. Cook slowly until ready.
4) Once in bed, I read for twenty minutes and then turned out the light.
4. Thus, I assumed the above 'being' might be left out but wasn't sure. With your pointing out now I've come to think this 'being' is needed even in an abbreviated subordinate clause, since the conjunctions like before, after aren't included in the list of above rule - a pronoun subject and the verb be can often be dropped.
I'm always really glad to have your nice and reliable comments, explanations whenever I suffer from problems.