Are the chainrings true? Drop the chain off the inside ring onto the BB and spin the crank by itself. Look down and use the FD as a guide. How straight does the chainring spin?

To test BB bearing-preload, line up one of the cranks next to a chainstay. Grab the chainstay with one hand and push the crank at the pedal end in and out to feel for play. You can also use the seat-tube as well, but its distance away from the crank makes it hard to see movement.

Chain rubbing the FD as you sweep across the rear-cluster is common. To have the largest sweep-range possible without trimming, you'll want to set your FD height and rotation precisely right as shown on this Park Tool - Front Derailleur adjustment guide.