Dill (cool-season annual herb) is classed semi hardy in the cited extension guidance. The timing rules below are relative to your local freeze dates — enter a location to turn them into calendar dates.
The rules this site applies
Method
Frost-relative window
Rule & reconciliation
Direct-sow outdoors
2–1 weeks before the median last spring freeze
Illinois: sow in spring one to two weeks before the last frost; Oklahoma State's Table 1 agrees (one or two weeks before).
No start seeds indoors window: Dill is tap-rooted and resents transplanting; the cited guides time direct sowing only.
Variety assumption: Leaf harvest begins about 40–55 days from sowing.