Toporovsky was born and grew up in Rishon LeZion. After completing his mandatory military service in the Israel Defense Forces, he studied law at Tel Aviv University. During his studies, Toporovsky became chairman of the university's student union in 2005, holding the post until 2007. He then entered politics and worked for Minister of Social Affairs, Isaac Herzog.
In 2008 he became chairman of the National Union of Israeli Students, and in the same year founded the Tzabar party, heading its list for the 2009 Knesset elections, in which it received only 0.14% of the vote and failed to pass the electoral threshold. However, the party did win seats on Tel Aviv city council. In March 2011 he became chairman of the Issta travel agency.