In the context of Albert Einstein's life, he didn't hope to get into an Italian college *without* a German school diploma. He *did* leave the Luitpold Gymnasium in Munich without graduating, but he *did* eventually obtain a Swiss Matura (a Swiss secondary school leaving certificate) which was then sufficient for admission to the Swiss Federal Polytechnic in Zurich. He then later attempted admission to the University of Zurich, requiring that Matura.
There's no instance where Einstein tried to gain admission to an *Italian* college without a comparable secondary school leaving certificate. While he spent time in Italy with his family, his academic pursuits focused on Switzerland. He wouldn't have been able to get into an Italian university, even then, without satisfying their entry requirements, similar to the Swiss or German systems.