Thyme (perennial herb) is classed hardy perennial 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
Transplant outdoors
from the median last spring freeze to 2 weeks after
Oklahoma State Table 1: plant thyme after the last spring frost (seed or cuttings; most gardeners set out plants). Point rule given a 14-day span.
No start seeds indoors window: The cited guide gives no indoor seed-starting lead time for thyme, so no window is calculated.
Variety assumption: A hardy perennial once established; harvest lightly the first season.