“g73, it seems to me that Rashi is saying that Yitzchok waited until she was 3 to marry her because she was then “raoi l’biah”; this implies that they did indeed “get married” when she was that age. At age 13, according to Rashi, Rivka was capable of becoming pregnant, so that Yitzchok waited 10 years from that point before concluding that she was an akarah. “
I think you have it backwards. The gemara derives the principle of “bat 3 shanim reuyah l’biah” since it is possible, based on calculations derived from the text that Yitzchak was 37 at the Akeidah and this Rivkah was three at their marriage. Yitzchak did not wait for Rivkah to turn three in order to comport with the Halachik norm. Rather the Halachik point is derived from his conduct. But that Halachik point really says nothing about the history involved. All it says is that since, theoretically, Rivkah might have been three at her marriage, a three year old girl is physically capable of biah (i.e. that the simanei betulah will not regenerate).