Divorce is a most despised permission to Allah, and it is incorrect for a Muslim to resort to divorce for the slightest excuse. In this case, there is no serious justification for divorce, particularly that the couple are at the first steps of married life. Indeed, it will lead to great harm affecting the woman and her reputation. Therefore, if the woman's justification is reasonable, as is the case in the question, the man ought to believe her. As it is possible that a woman may lose her hymen when practicing some sports and by being careless or even reckless with physical activities and so on.
If the woman swore by Allah Almighty that she had never had a sexual relationship prior to the marriage, the man must belief her as the famous legal principle is "proof is to be submitted by the accuser and an oath is to be made by the denying accused". The husband in this case is the accuser with no proof, whilst the accused, i.e. the wife, has made an oath denying the accusation, and thus, must be accepted. In any case, our Islamic dealing is based upon the principle of trust and good-will towards people, as suspicion is indeed sinful.
However, even if we assumed that the woman made a mistake in the past, then repented and returned to Allah; we know that Allah will accept her repentance and that this dissolves all her previous sins. Indeed he whoever repents from a sin is as though he has made no sin at all. It is upon us to forgive those who err, as all sons of Adam err, and the best of those who err are those who repent.