Many headsets have a rubber seal ring under the outer cap which drags on the rim of the headtube. A small amount grease on this ring will cure your squeak.
It won't need full disassembly; just loosen the stem clamp bolts & the top cap enough to lift the stem & bars a few mm, work a bit of grease under the bottom edge of the outer headset seal (this may be a conical cap/spacer, especially if it's on a Giant), then tighten it all back up. Top cap first, enough to ensure that there is no play in the headset but still running freely, set the stem/bars straight & tighten the bolts, preferably with a torque wrench.
Just ride the bloody thing and enjoy yourself!