You can leave and re-enter, as long as you have with you the postal receipt for the permesso application, and follow the additional stipulations listed by the Polizia di Stato.
Note that the procedure is the same for those awaiting their first permesso, as for those who are renewing (emphasis mine).
Requirements for immigrants leaving Italy temporarily
Foreigners awaiting renewal of their residence permits can leave and re-enter Italy if they hold:
- the receipt issued by Italian Post offices (Poste Italiane S.p.A) certifying the submission of the application for renewal of their residence permit or EC residence permit for long-term residents;
- the expired residence permit;
- their passport or other equivalent travel document .
The same facilitated procedure is granted to foreigners who have submitted their application for their first residence permits for employment, self-employment, or family reunification, provided that:
- they leave and re-enter Italy through any Italian external border crossing point (circular letter 11th March 2009);
- they show their passport or other equivalent travel document, along with the entry visa specifying the reasons of their stay (employment, self-employment, or family reunification ) and the receipt issued by Italian Post offices (Poste Italiane S.p.A.);
- they do not transit through other Schengen countries, as this is not allowed.
The circular letter (pdf 35 Kb) of 27 June 2007 states that foreigners who have children under the age of 14 may request the Questura to issue a temporary residence permit with limited validity. This document will contain the personal details of the children who will then be allowed to leave Italy temporarily.