Cancer is a potentially lethal disease, in which patients with nearly identical genetic backgrounds can develop a similar pathology through distinct combinations of genetic alterations. We aimed to reconstruct the evolutionary process underlying tumour initiation, using the combination of convergence and discrepancies observed across 2,742 cancer genomes from nine tumour types. We developed a framework using the repeatability of cancer development to score the local malignant adaptation (LMA) of genetic clones, as their potential to malignantly progress and invade their environment of origin. Using this framework, we found that premalignant skin and colorectal lesions appeared specifically adapted to their local environment, yet insufficiently for full cancerous transformation. We found that metastatic clones were more adapted to the site of origin than to the invaded tissue, suggesting that genetics may be more important for local progression than for the invasion of distant organs. In addition, we used network analyses to investigate evolutionary properties at the system‐level, highlighting that different dynamics of malignant progression can be modelled by such a framework in tumour‐type‐specific fashion. We find that occurrence‐based methods can be used to specifically recapitulate the process of cancer initiation and progression, as well as to evaluate the adaptation of genetic clones to given environments. The repeatability observed in the evolution of most tumour types could therefore be harnessed to better predict the trajectories likely to be taken by tumours and preneoplastic lesions in the future.