Final answer:
The organism most likely responsible for causing endocarditis in a patient after dental surgery, without knowledge of their existing heart condition, is Streptococcus viridans.
Step-by-step explanation:
The patient who had dental surgery and subsequently developed endocarditis likely contracted the infection from Streptococcus viridans, a bacterium normally present in the mouth. During the dental procedure, the patient's gum may have been nicked, providing a pathway for the bacteria to enter the bloodstream. Endocarditis caused by S. viridans tends to progress more slowly, which is consistent with subacute bacterial endocarditis, characterized by the formation of vegetations on the valves over time. This type of endocarditis can greatly damage the heart valves and may necessitate valve replacement if not treated promptly with appropriate intravenous antibiotics.