Transposable elements (TEs) face significant challenges upon transfer into a new host population, invariably beginning their invasion with only a single element. The fate of this element is a product of its internal properties, the population dynamics of the host species, and genetic drift. We present a continuous-time multi-type branching process to model the early stages of TE spread. The model incorporates seasonal population size changes and is applicable to diploid hosts for prevalences up to 10%. We reproduce standard results of TE population dynamics and show that population growth may have a greater influence on reducing TE loss probability than a transpositional burst. These results are applied to the planned use of a TE to drive an antimalarial gene into an Anopheles gambiae population. The model favors a transgenic release immediately following the dry season when the An. gambiae population begins to grow. Increasing the number of transgenic hosts released has the greatest influence on reducing the probability of TE loss. Following release, the rate at which the TE increases its proportion in the population is most sensitive to its replicative transposition rate. The model recommends a replicative transposition rate greater than 0.1 per TE per generation to satisfy public health goals.