How long does sepsis take, after infection?

Not long. It can take as little as 30 minutes to acquire the signs of sepsis. Even spetic shock can occur very quickly if the conditions are right.
Quickly... Once bacteria get into the blood, depending on the bacteria, its inoculation size, and its virulence, the development of all the signs and symptoms of sepsis can develop quickly, as is seen with staphylococcus aureus and streptococcus pyogenes infections.