Is it permissible to falsify one's age in official documents in order to join a sports club, knowing that this would not harm anyone?

Lying is forbidden (haram) and leads to immorality, and then to the Fire. Persisting in it causes its perpetrator to be recorded as a liar with Allah. It is not permissible to lie to obtain this opportunity. Rather, missing it might be better for a Muslim, because this field is not something that pure, pious souls aspire to.