Let's be friends!
'Amicizia' = a-mi-CI-zia, stress on third syllable. 'Facciamo' = fac-CIA-mo.
Use this as a direct and warm declaration after a very positive first meeting. It is slightly bold but completely natural in Italian social culture. It is especially common among young people and children, but adults use it too in enthusiastic social moments.
'Fare amicizia' (to make friends) is the Italian expression for becoming friends. 'Facciamo' is the first-person plural: 'let's make/do'. It is an enthusiastic declaration of intent. You can also say 'voglio diventare tuo amico/a' (I want to become your friend).
Siamo già amici!
We are already friends!
Even bolder — declaring friendship has already happened
Voglio che diventiamo amici.
I want us to become friends.
More considered and intentional expression
Penso che potremmo diventare buoni amici.
I think we could become good friends.
More tentative, conditional — slightly less direct
Italian friendship ('amicizia') is considered one of the most important values in life. The distinction between 'amico' (true friend) and 'conoscente' (acquaintance) is sharp and important. An Italian who calls you 'amico mio' (my friend) means it deeply. True Italian friendship involves loyalty, mutual support, and lifelong bonds.