Can left ventricular hypertrophy occur suddenly? from like an infection or is it only gradual?

Yes: Gradual LVH is mostly from hypertension or heart valve problems. Lvh can occur more rapidly in conditions like hypertrophic cardiomyopathy (commoner), or "infiltrative" conditions where abnormal substances are deposited in the heart muscle (rarer). However, I am not aware of an infectious cause of lvh.

Not usually sudden: Hypertrophy is enlargement of the hart muscle. It can be a normal response (like to athletic conditioning), or due to abnormalities in the muscle that leads to the hyper trophy. Either way it develops over time. It is seldom, if ever, related to an infection. Infections are more likely to lead to dilation of the heart, not hypertrophy.