Would the Arcane Archer's Arcane Shot (Xanathar's Guide to Everything ch. 1; link requires access to XGtE in D&D Beyond), made using a nonmagical bow and a nonmagical arrow, count as a magical attack for purposes of overcoming a monster's resistance or immunity to damage from nonmagical attacks?
Only the effect applied by Arcane Shot overcomes non-magical resistance
As per the description given:
Once per turn, when you fire an arrow from a shortbow or longbow as part of the Attack action, you can apply one of your Arcane Shot options to that arrow.
And the options themselves:
Arcane Shot Options
The options are all magical effects. If an option requires a saving throw, your Arcane Shot save DC equals 8 + your proficiency bonus + your Intelligence modifier.
The options themselves are magical effects; therefore, they are the only part of the attack that overcome non-magical resistance. Arcane Archer later gets a 7th-level feature, Magic Arrow, that allows you to make your attacks magical for the sake of overcoming resistance.
See also this post on determining what is and is not a magical effect.