Which is correct or sounds better to you?
It will take a while until the change takes an effect.
It will take a while before the change takes an effect.
Both are valid, but have slightly differing connotations. "Before" seems to stress the span of time preceding the effect; "Until" seems to stress the change that will be effected after that span of time.
Additionally, I agree with FumbleFingers that the phrasing is awkward. His phrasing is a good alternative. Else you can rephrase it "It will take a while for the change to be effected." This eliminates the need to choose between your alternatives, but makes use of passive voice, which is of contested validity. Personally, I have never had a problem with its usage, but that is something you must decide for yourself, based on personal preference and the context for which you are writing.