Smoothing down adhesive stickers takes practice and finesse.
In general, it is best to start in the center and work radially outwards.
Flat surface to flat surface, you can sometimes start at a corner and use a straightedge to move across in a line, but that will not work here because your are inset in a depression.
My first try, in your case, would be to bend the sticker around a cylinder (ie my index finger) and touch down in the center. Then I would sweep sideways each way, then vertically each way, then diagonally.
Keep each stroke firm but gentle, and remember not to stretch the sticker unevenly in any direction.
Once down, I would burnish outwards from the center in a spiral, with a fabric layer on my finger to reduce friction.