Eldritch Darts doesn’t require a test to cast. Spell Supplies add +1D to the casting roll. In this case, is that +1D bonus made to the Arcanist roll in the first round of combat they are used?
I would say “casting roll” equals “attack action” in case of Eldrich Darts.
So any time you do it, you can use spell supplies, thought they will affect just specified roll.
(any combat round, maybe multiple times, if you have such a stash of supplies)
Or I can see that it could be interpreted even broader, maybe that’s left up to GM.
Supplies after all are not cheap to carry.