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Polish it with a machine as said,but G3 might be a bit harsh btw and cutt far to much paint away than needs be.
And if you want a good finish follow up with a finishing polish,top up with a wax or sealant reqular to stop it fading again.
Hows about AutoGlym super resin? its not very harsh but does have cutting properties
it's a reasonable product, no comparison with machine polish and a medium pad/compound and can be a bit chalky with the fillers in it.
before a machine AG SRP then over with meguires carnuaba wax made my old diamond white xr2 shine really well, but was a lot of work by hand.