The encounter was the beginning of a life-long tie with the Frank family, which was to shape Eva's entire existence.
Just a month apart in age, the girls played together in a large group, unaware that the diary Anne kept would later become the second most widely read book in the world after The Bible.
Both girls went into hiding for many months in a bid to escape anti-Semitic persecution by the Nazis – and both were later captured and imprisoned in brutal concentration camps.
As we know, Anne Frank did not survive, dying, alongside her sister, Margot, in concentration camp Bergen Belsen in April 1945, just a few weeks before the camp was liberated. Eva, though, did survive, and became Anne's stepsister some years later, when her mother married Anne's father, Otto.
Eva, now 82, has dedicated the past 25 years of her life to educating youngsters about the Nazis' persecution of Jews, predominantly through her play, And Then They Came for Me which was performed in Scotland yesterday to mark Holocaust Memorial Day.
The play is told through both real-life interviews with Eva and Helmut "Ed" Silverberg – another Jewish refugee living in Amsterdam and an admirer of the young Anne – as well as actors playing the three teenagers and Eva's brother Heinz. It charts the years between 1940 and 1945, when Hitler's regime was at its strongest, and was shown to youngsters at Larbert High School, near Falkirk.
As young girls growing up on opposite sides of the Merwedeplein square in Amsterdam, the pair were not great friends. Eva describes Anne as a "pretty" and "talented" girl, but also insists they were very different. Anne was into boys, fashion and film stars – this is backed up by Silverberg, who, three years Anne's senior, says in the interviews in the play that he fell in love with the 13-year-old during the year before she went into hiding – remembering her "flirtatious" body language and a desire to be the centre of attention.
Indeed, Eva's portrayal of Anne in the play is one of a self-confident, overly dramatic teenager, with high opinions of herself and her talents. Eva, in contrast, is humble and quiet, preferring the company of her small, close-knit family to the "crowds of friends" Anne liked to surround herself with.