If you are in Chatham, Kent, England, this is a problem that Brian Rodgers has been known to fix.

First stage is to play all the strings one at a time at every fret up and down the neck to see if they do it on their own. If you find a buzz anywhere doing that, suspect the frets in that area. It's perfectly normal to have to dress the frets just a little bit on a new guitar.

Next step is to enlist a third hand (not a capo), and have the third hand press firmly on each string between the bridge pins and the saddle while you play, to see if it's saddle buzz. Unlikely if you have had the saddle up and down looking.

If the buzz goes away when you capo at the first fret, suspect that the nut slots have been cut too deep. Unless they are MUCH too deep you would usually expect such a buzz to go away if the truss rod was slackened off and/or if the saddle was raised.

An alternative is nut slot buzz. Have a friend with a pointed object press each string in turn firmly into the nut slot while you play. Or you can lift each string in turn and pop a bit of paper in teh slot just to try.

Lots of things can rattle on a headstock. A loose string-post nut, a loose helix in a machine head, a loose tuning button on a shaft, a string-tree.

Has the guitar an internal pickup? Have you checked where the wires are?

Can you cause buzz or rattle by drumming with your fingers on the top of the guitar (go carefully and systematically round) - a brace may have come loose - or a bit of kerfing.