There is a difference in meaning and usage between 「うちに」 and 「うちから」.
「Situation + うちに + Action」= "to complete an action while a certain situation is in progress"
「Situation + うちから + Action」 = "to perform an action before something happens"
「うちから」 generally implies the speaker's opinion/judgement that it is a bit too early to perform the action. It has a negative vibe to it.
「うちに」, however, is more neutral as far as the positive or negative connotations it creates.
「おとうさん、何も起こってないうちからわざわざ断言することないでしょ。」
thus means:
"Dad, you don't have to go out of your way to declare that before it happens, do you?"