Premarital sex is sex that occurs prior to marriage. It has been argued that "Previous sexual experience with a partner weakens mutual commitment in marriage and creates an unstable foundation for the conjugal relationship."  Jim Duley notes that in the past, premarital sex did not exist:
[F]or much of Jewish and Christian history having sex was one of the ways you got married in the first place. Civil marriage licenses were invented quite recently (beginning in the 17th century). Only the wealthy had "weddings" in the sense we have them today. People simply moved in together (the bride went to live with the groom's family) -- sometimes with ritual and sometimes without any at all. The obsession in some cultures with the virginity of the bride has real roots in determining whether she was not "already married" -- that is, the "possession" of another man "acquired" by sexual intercourse.
In the early part of the Christian Era, Jewish scholars compiled the Talmud, a foundation of Jewish law. In the Talmud it is clear there were three ways to solemnify a marriage: by contract (between families generally), by gift or by sex. As early Christianity is deeply tied to Judaism, it us likely that early Christians had similar practices, since the Talmud generally reflected what was going on already. It didn't create new customs or laws for the most part.
By the Middle Ages, Jewish sages noted that customs (not laws) had changed to the point that marriages were being entered into only by the first two methods - and generally both - which is why men gave their bride a ring (a gift) and the witnesses signed a ketubah (a wedding contract). Vestiges of the third method still remain in the chuppah - the wedding canopy - symbolizing the marriage tent / bed. The fact that Jewish couples often enter a brief isolation together after a wedding (now generally to reflect on what they just did and perhaps grab a quiet bite to eat) is clearly an evolution from what started as a consummation of the marriage.
So, at some level Christianity could "solve the problem of" premarital sex by going back to its roots and simply recognizing that historically these people may actually already be seen as married in he eyes of G-d. It would certainly save their parents all the trouble of hiring a caterer and a DJ.