How long does it take for FCoV to mutate and cause FIP in infected cats?
The short answer is: We don’t know.
The long answer, is below, courtesy of Ms Aurora Carreira Miguel, founder of Project Fight FIP in South Africa, and co-founder of FIP Advisory and Care Group.
This question has no 100% clear answer unfortunately as it is not really known. From https://www.msdvetmanual.com/generalized-conditions/feline-infectious-peritonitis/overview-of-feline-infectious-peritonitis
After a cat becomes infected with FCoV via fecal-oral transmission (or less commonly, inhalation), the main site of viral replication is the intestinal epithelium. Replication of FCoV in the cytoplasm can destroy intestinal epithelial cells, leading to diarrhea in some cats. In many cats, infection persists for weeks to months in the absence of clinical signs. These cats shed FCoV either intermittently or continually and act as a source of infection for other cats. Previously, it was believed that avirulent FCoV remained confined to the digestive tract, did not cross the gut mucosa, and did not spread beyond the intestinal epithelium and regional lymph nodes. However, PCR can detect FCoV in the circulating macrophages of healthy cats from households with endemic FCoV, indicating that avirulent FCoV may also cause viremia.
The length of time between infection and development of clinical signs is unknown and depends on the immune response of the individual cat. Disease generally becomes apparent from a few weeks to 2 years after the mutation has occurred. Cats are at greatest risk of developing FIP in the first 6–18 months after infection with FCoV; the risk decreases to ~4% at 36 months after infection.
What is FIP: https://www.endfip.com/what-is-fip/
Virus pathogenesis: https://www.endfip.com/virus-pathogenesis/
The vast majority of cats infected with FCoV do NOT develop FIP, but become infected, shed virus in their feces from 2-3 days post-infection, seroconvert (change from negative to positive) at 18-21 days, stop shedding the virus after 2-3 months to 7 months, then lose their antibodies. About 13% of infected cats become lifelong carriers, continually shedding FCoV in their feces and maintaining a high antibody titer. Natural immunity to FCoV is poorly understood but is presumed to be cell mediated rather than antibody mediated. The earliest FIP occurs is at around 28 days post-infection, and there is usually a history of stress such as having been rehomed or spayed/neutered. Effusive or wet FIP is the acute form, occurring 4-6 weeks post-stress and non-effusive or dry FIP is the chronic form and can occur months to years after infection. In effusive (wet) FIP many blood vessels are damaged, and in non-effusive (dry) FIP the immune response has been partially successful, walling off the infected vessels with pyogranulomata which can become quite large (in abdominal palpation and gross postmortem they can be mistaken for tumors).