Only way
The only way to improve the appearance of those scratches and the pitting
Is to use some thing abrasive, If you try to polish straight you won't make any impact unless you polish like a maniac multiple times, it'll be shiny but scatched
You'll get somewhere with wet and dry but it will be very hard going, but safe. You don't want to dig away at those tubes!
Happilly, looks like all those scratches are very shallow
I have a seat post which looked far worse than your pic I improved it's appearance with fine sand paper, then wet and dry, then autosol (regular)
The black spots are scars from the pitting which was underneath corrosion which had occurred becasue of crud on the suface
As you can see, LGF is right, these 'raw' finishes will oxide back up, if they are kept clean they will remain looking good, but go flat takes a good while though That seat tube is now 'silver' did look dazzling about a year ago
This is due to an oxide layer forming on the surface of the aluminium
This layer is damned tough and actually preventss corrosion problems occur when crud sits next to the surface the aluminium and can eat away at this/prevent it reforming - or harsh environments like the sea!
I could spend 3 minutes with a rag and T-Cut and it would be dazzling again
Here's my Zaskar, it was never mirror polished, but this is how it looks after commuting through all the snow and salt gets cleaned every couple of weeks, not polished though I did polish it long ago when it looked unbearably ropey, so beleive me I know your position
If you do want to mirror polish, you'll be surprised how easy it is to maintain there are a good few GT owners on here who have dazzling bikes! But I thinh like my seat post your GT will have a few acne scars
I have a build in progress which is destined to be mirror polished raw aluminium
It was lacquerd so I stripped that then wirewooled it using brillo soap pads with autosol and T-Cut on them
Next just Autosol
I'm going to T-Cut it for the full on mirror shine once i have te energy
I didn't use sand paper on a frame and wirewool has the massive advanatge that you can douse it in other goodies and it's flexible, fits really well round curves and into tube junctions...
Nearly there!
So I'd recommend the same to you, start with wirewool it'll go ll gray but hopefully flat, then autosol, then something really gentle like T-Cut or Brasso as most others have said. However for the heavy artillery, on any massively scratched parts used cautiously sand paper could save a lot of arm ache
I think the ball burnished finish is a goner I'm afraid