Another popular method for removing small amounts of copper from an aquarium is to have (activated) carbon in your filter medium...
I've read one study whereby the carbon could be regenerated / stripped of the copper by later use of acetic acid or even white vinegar (weak acetic acid.)
I wish I had a link handy.
One note is that the study didn't mention saltwater with copper.
Not saying you can't go have fun with the other methods given so far...
But I know for my fish tank I hate having to actually remove all the water.
Let alone the sand, or the plants.
The (activated) carbon is a pretty common medium to obtain at fish stores, and even major chain stores.
You may want to try using distilled water, rather than water from the pipes if that is where your copper is coming from...
Ignore that, as I misread your original post. Your copper came from a brass fitting, and you were 100% certain that it was not in the water you used.
That 'enahs' is right, imho, don't add the live coral, non feeder fish, or most plants until the tank is established.
>>
I personally would just clean everything really well with a lot of hard scrubbing and lots of water to rinse, and then setup the tank without putting the expensive reef and sands in, and let it pump for a few days and see if any accumulate if you are really worried.
<<
For freshwater tanks I would probably wait at least a week, just to make sure that all the exciting microrganisms are ready as well.
I haven't done anything with saltwater tanks, and brackish water fish only in bowls.
Nick