I understand that "estamos" is "we are", but most native English speakers I know would rarely express it as "We are already in June". We would just say "It is June already". It's similar with temperatures, like "Estamos veinte grados". We would say "It is twenty degrees", not "We are twenty degrees".
Something you need all to understand is that we don't only learn vocabulary, we learn a new language.. Of course there is a different way to say things in an other country. This sentence is translated word by word so you can understand what it means without saying it's a common expression in english.. You just have to start thinking spanish not english. :)