The headstock end of the truss rod should be fixed to the neck somewhere around the 1st fret, so you shouldn't see any variation between the 1st fret and the nut, so in theory it should be having some effect between the 1st and 3rd frets, but if the fretboard has a physical dip in it at that point, then there's not a lot the truss rod can do to fix that as the rest of the neck will be moving relative to it.

The full pro-level solution would be to remove the frets, level the fretboard and re-fret. But that's quite a task!

Use a straight edge and see how big a gap you've got between it and the first couple of frets,as that's how much the other frets will will need to come down; or at least the 3rd fret, with the others reducing in height reduction as you go up the neck. You want the tops of the frets level, but you can allow the fret height to vary (though this is not the ideal it is practical). In effect you want to draw a straight line between the first and last fret, and take the tops off the other frets until they reach that line, with the most coming off that 3rd fret. Easier said than done though without running up quite a complicated jig.

So you may want to sand or file down the 3rd fret on its own e.g. 20 rubs, then sand the 4th fret down a little bit less e.g. 19 rubs, the 5th a little bit less again etc. Then use an overall sand with the level to even things up as much as possible.

Or whatever works for you and you feel happy doing.