What did Roman structures look like before accepting Greek culture?

There really aren't any. Roman architecture was heavily Etruscan-influenced before it became effectively Hellenistic, but Etruscan architecture, too, borrowed a lot from the Italiote Greeks. What it looked like in its 'authentic' state is hard to deduce, and probably the wrong question anyway. Rome grew up in a heavily Greek-influenced environment from the first day. Fascist imaginaries of an original Italian culture overlaid with Greek fripperies just don't do historical reality justice.
 
Rome was influenced by Greece from very early on, if you want a primal latin look, try checking out the Etruscans.

The Etruscans weren't latin. As a matter of fact, the Etruscan culture brought to the latin culture many things we suppose to be "Roman": the alphabet, the architecture, the religion, the politics etc.
 
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