I cannot think of words beginning with a silent c.
There are many with a silent c in their structure: ascent, scent, descent [and many others].
see here for more information: AskOxford: Silent Letters
I would like to find some words begging with silent "C"
Only one I can think of offhand is actually a Yiddish word but it is used commonly in English: chutzpah. Pronounced "hootzpah."