The Scriptures warn against placing someone rather new to the faith in a position that might tempt them to be puffed up with pride:
I Timothy 3:3 This is a faithful saying: If a man desires the position of a bishop, he desires a good work. 2 A bishop then must be blameless, the husband of one wife, temperate, sober-minded, of good behavior, hospitable, able to teach; 3 not given to wine, not violent, not greedy for money, but gentle, not quarrelsome, not covetous; 4 one who rules his own house well, having his children in submission with all reverence 5 (for if a man does not know how to rule his own house, how will he take care of the church of God?); 6 not a novice, lest being puffed up with pride he fall into the same condemnation as the devil. 7 Moreover he must have a good testimony among those who are outside, lest he fall into reproach and the snare of the devil.
I Timothy3:
However, that is not totally about age, as Timothy was not to let people look down on him because of his youth.
4:12 Let no one despise your youth, but be an example to the believers in word, in conduct, in love,in spirit, in faith, in purity.
Timothy by this point had already ministered along with Paul and others for some time, and was known to be faithful, filled with the Spirit. He was mature in Christ at a young age, and so left by Paul in Ephesus with a task to undertake.
Also, as Paidiske indicated you build experience in the faith by doing, often with those who have been in the faith for some time and are mature. So a position of authority might not be warranted, but being allowed to minister in various ways, with direction, could be quite helpful, and we see biblical examples of this happening with a young person such as Timothy. And if he already has shown the Biblical character requirements, showed gifting, and has been ministering faithfully, then it may be possible for someone even of a relatively young age to be given some authority, as we see with Timothy. Even here it is in the context of Paul mentioning that he hopes to join him soon, admonishing him to be faithful, etc. Paul is still giving direction.