By studying a recent biophysical model of tumor growth in the presence of the immune system, here we propose that the phenomenon of evasion of tumors from immune control at a temporal mesoscale might, in some cases, be due to random fluctuations in the levels of the immune system. Bounded noises are considered, but the Gaussian approach is also used for analytical reference. After showing that in the case of bounded noises there may be multiple attractors in the space of probability densities, we numerically show that the velocity of convergence toward asymptotic density is very slow and that a transitory analysis is needed. Then, by simulations using the sine-Wiener and the Tsallis noises, we show that if the level of the noise is sufficiently large then there may be the onset of noise-induced transitions in the transitory density evaluated at realistic times. Namely, the transitions are from unimodal density centered at low values of tumor burden to bimodal densities that have a second maximum centered at higher values. However, those transitions depend on the distribution of the noise.