Start thinking about your thesis research project as early as possible, e.g., by developing research expertise through UROPs. Be alert to interesting problems that come to your attention in class, personal contacts, or through the technical literature. By doing several UROPs early on you will learn about research areas that do NOT interest you, which is invaluable.
Undergraduates planning to continue for the MEng should get involved in a research group (through UROP, initially) as early as the sophomore or junior year. It is particularly important for students interested in continuing for the Ph.D. to gain exposure and experience in research. (Being involved in a research group long-term is the best way to improve chances for funding as a Research Assistant for the MEng, although of course there are no guarantees.) Some faculty feel that there is a long period of apprenticeship during which the student's training requires more effort than is returned by the student's labor. Only after this period does the 'payback' begin. It is in that 'payback' period that most supervisors expect to find the student's M.Eng. thesis work.
It is vital to have a thesis supervisor by the time you switch to graduate status, or very shortly thereafter. You are expected to register for thesis each term in MEng, make significant progress, and submit a proposal no later than the end of your first graduate term. Failure to submit a proposal after more than one term may result in removal from the MEng program.