Traditional Christian culture says that all sex outside marriage is immoral, and my understanding is that this has been true throughout history. However, I'm curious if my assumption is correct. Has there ever been a period of time in a culture that identified as Christian where most couples did not get married?
I don't know about marriage, but Shakers aren't allowed to have children and they are a Christian sect.
There were definitely Christian movements and subcultures that didn't marry because they wanted to maintain celibacy. It appears that this may have been relatively common in the early church. Several of the Apocryphal Acts have the eponymous apostle causing trouble for himself by getting a betrothed woman to break it off with someone in a position of authority.
But if we're talking about people who plan on being sexually-active, no, I don't believe that's ever been the case. Marriage is ubiquitous in all cultures and is not so much a product or aspect of religion as something appropriated by it. Marriage would exist because ancient cultures needed a division of labor in the household, wanted to form clan-based social groups, and saw women as property or dependents who needed to be shepherded by men. Up until our time, it would have just been impractical or extremely counter-cultural for a society to not have practiced something like marriage, regardless of whatever the particular beliefs were about sexuality.