We are told that Max Vandenburg is age 22 on the Kristallnacht (or the Night of the Broken Glass) on November 9, 1938, when the Nazis destroyed many Jewish businesses and synagogues. Kristallnacht "proved to be Max Vandenburg’s moment of escape. He was twenty-two."
Because of this event, Max goes into hiding. His mother gives him Hans' name and address as a person to turn to in a time of need. In 1939, Max reaches out to Hans. In mid-May of 1940, Hans sends him a copy of Mein Kampf with a key taped inside. At some point later, Max finally arrives at the Hubermann residence, ending up living in the basement there and meeting Leisel. Because he is 22 in late 1938, he must be 24 years old or older when he takes refuge with the Hubermanns.
As the novel points out, it is risky for the Hubermanns to harbor a Jew in Nazi Germany. It's also worth noting that Max is a good deal older than Leisel, approximately ten or more years her senior. Nevertheless, he and Leisel appear to fall in love. It is implied, though not stated, that they marry after the war.