Reviews.com presents a guide to filing insurance claims, and cites WCRI research:

How long does it take to settle a claim?
Time to settlement depends on severity, documentation speed, adjuster/repair capacity, and whether a catastrophe (CAT) surge is in play... In workers’ compensation, the first temporary‑disability payment typically arrives two to three weeks after injury, varying by state (WCRI).

The WCRI research they cite is CompScope™ Benchmarks, 2025 Edition.  Click the link for more information, including links to the individual state studies and details on how to get copies!