I understand that sepsis can take hold very quickly. however, is it possible for there to be a "smouldering" sepsis that can take 2 or more weeks to develop to be immediately life-threatening?

Yes: If there is an infection that is closed off in some way like an abscess or an infected heart valve you can have intermittent fevers and symptoms like that. See your primary care sources can be hard to find sometimes he/she can decide if studies are needed.

Yes.: Explanation could be long but i will try to make it short. An infection could be under control temporarily and just "tug along" and take for example an abscess. When the body loses its ability to keep the infection in check along with antibiotics at times, then sepsis sets in and could only take a few hours and can become overwhelming. Development of antibiotic resistance can also be considered.