Do Muslims believe that the moon was split in two and put back again?

According to this:- https://islam.stackexchange.com/questions/37680/does-the-quran-or-any-hadith-mentions-the-splitting-of-the-moon It's mentioned in the Quran that the moon was split into two. As the Quran is perfect and infallible, then Muslims must believe that the moon was indeed split into two and put back together again. How is it possible that no other culture/civilization has a record of the moon being split into two? It was a time when people carefully observed and recorded even phenomena such as solar/lunar eclipse, since they were largely unexplained back then.