IMO Livor mortis is not immediate.
Lividity is important to the investigator for two reasons. First, it can provide investigators with a general understanding of the time since death. These estimates are influenced by things such as temperature, body mass, conditions at the crime scene, and other factors. Suffice it to say Im only giving you very general time frames but for your novel they should be fine. Lividity is generally seen within the first 1-2 hours following death. It will typically become fully developed within 3-4 hours but could still be altered if the body position changed. After 12 hours the lividity becomes fixed meaning it will not change.
http://forensics4fiction.com/2011/06/06/estimating-the-time-of-death-livor-mortis/
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