It should either be "We start school in July" or "We start at the school in July"
I have never seen "We start at the school." "We start school" is simply a set phrase, at least in American English.
I would depend on the context. If you were talking about starting at a particular school, instead of just starting school you'd be very likely to say "We start at the school" in Australian English anyway. This might not as good a translation though.
With the "the" it sounds like you're about to start a project such as constructing a school building. In August, we start the library!
Since Masuk means To Enter (rather than To Start), does it actually mean kids starting to go to school the first time in their life?