Pointless sidenote - my gorgeous Latin teacher for two years in high school, Mrs. Ross - she was convinced that the Romans didn't have 'soft c' technology and therefore we always had to pronounce your handle "KICKero." She also figured that their v's sounded like w's. I have no idea how she knew this stuff.
Mrs. Ross was right! That’s the pronunciation of Classical Latin, as opposed to Church Latin, which came later.
We know those were the original pronunciations because of historical linguistics, which allows to predict original sounds based on how the sound evolved in modern Romance languages like Italian, Spanish, French, etc. And also we have direct evidence from the time period too. The Greeks, for example, wrote Silouios (Sil-wee-os) for Latin Silvius.