Cancer is a set of genetic diseases that result from accumulation of unfavorable mutations. As soon as genetic and epigenetic modifications associated with these mutations become strong enough, the uncontrolled tumor cell growth is initiated, eventually spreading through healthy tissues. Clarifying the dynamics of initiation is critically important for understanding the mechanisms of cancer. Here we present a new theoretical approach, stimulated by analogy with chemical reactions and other stochastic processes in physics and biology, to evaluate the dynamic processes associated with cancer initiation. It is based on a discrete-state stochastic description of the formation of tumors as a fixation of unfavorable mutations in populations of tissue cells. Thus, the main idea is to map complex processes of cancer initiation into a network of stochastic transitions between specific states of the tissue, like chemical reactions networks. In other words, a specific free-energy landscape for cancer initiation is postulated. Using a first-passage analysis, the probabilities for cancer to appear and the average times before tumor appearance are explicitly calculated. The method is applied for estimating the initiation times from clinical data for 30 different types of cancer. It is found, surprisingly, that the higher probability of cancer to occur might not necessarily lead to the fast starting of the cancer. It also suggests that cancer initiation process probably proceeds via an effective “free energy” barrier, which might be a target of future anticancer treatments. The similarity of the mechanisms of cancer initiation processes with dynamics of chemical reactions and stochastic processes are discussed. Furthermore, it is shown that the order of mutations might lead to different cancer initiation dynamics, explaining surprising experimental observations that order of mutations can affect the cancer outcome. Our physical-chemical view of cancer initiation as a motion in the effective free-energy landscape provides new insights into the mechanisms of these complex processes.