The word كدع 'brave' doesn't seem to be related to the MSA root كدع 'to push back, shoo away, push away'.
Any idea on the origin of the word كدع in Levantine Arabic?
إنها من السريانية gadoûda: اسم دلّ على المراحل التي تسبق الزواج، بها يكون الشاب غير مبالٍ ويقدم على أعمال بطولية لا يجرؤ الشيوخ على القيام بها. وغالباً ما تنطق الكاف كالجيم المصرية.
It is from the Syriac word gadoûda: the name of the pre-marriage stages, in which the young man is indifferent and does heroic deeds that the elders do not dare to do. And the ك is often pronounced like the Egyptian ج.
It's probably just Arabic جذع (notwithstanding the Syriac cognate), which means young person. It appears in Egypt as جدع and in the Arabian peninsula as جذع.