I love this question! I'm not sure that I can give a perfect answer -- but I'll try to give a good one.
In a sense, Rome has been built from several hundred B.C. to the present day. But the main buildings of Rome, at the height of its power, were built over approximately 300 years -- 100 B.C. to 200 A.D., give or take a few years.
You can see a timeline of Roman architectural history on this page.