Shower doors don't fit on shower base
Unfortunately while your shower door and base look nice, the engineering on them is whack.  Just looking at where the door should sit... its not even flat.   I am guessing (hoping) that there is a bevel to the bottom of the door that makes it &quot;fit&quot; but just a flat surface works better.
I have put in 10s of these things.   On all of mine I have had the OPPOSITE issue. I have to build out to a depth so the door isn't inside.
What could you have done better?     Well you should have set your base up and put the door on to test out the dimensional fit before installing the backer and tile.   If you are off by that much there is no way this thing will fit.
(pre) Solution?   You could inset the wall compared to the rest of the room by using thinner concrete backer or possibly make the rest of the room thicker...   You could also push the base out by maybe adding a backing to it.   It is too late to try these things as you would need to rip out your base and redo plumbing a bit.
(post) Solution?   You cannot cut out a space for your door.   I have no idea why that is being suggested in the comments.   I have never seen anyone with any tool that could cut out tile in a straight line.   Sure you can cut it out.   Just like I can spray paint my car myself when I need a paint job.   Expect to use lots of caulk after and for it to look really bad and possibly leak.
Me guesses... I would guess that the manufacturers run sheet on this install is doing it with a PVC wall system.   I am guessing that they suggest that the walls go right on the 2x4 framing.  Then your door fits.   There really isn't another way given your details are correct.    (do you have the manufacturers install instructions for this? it is common for these bases/doors to be sold separate from a wall system as they can give you a variety of choices on the wall system.)
How do we salvage this?   The only solution without ruining the integrity of the tile work you have done and possibly ruining the waterproof system is to cut the door to make it fit.   Cutting the metal is not that big of a deal.   The cuts should be hidden for the most part and the side pop back in after.   If you can only cut one side obviously that is half the work but I am not there and doubt it.   The problem is you probably cannot cut the glass as it should be tempered.   Meaning local glass shop will have to send out two new tempered sheets.   So your cost of repairing this right is really just those two new sheets (100-150 in my area).