Feature engineering is widely acknowledged to be pivotal in tabular data analysis and prediction. Automated feature engineering (AutoFE) emerged to automate this process managed by experienced data scientists and engineers conventionally. In this area, most — if not all — prior work adopted an identical framework from the neural architecture search (NAS) method. While feasible, we posit that the NAS framework very much contradicts the way how human experts cope with the data since the inherent Markov decision process (MDP) setup differs. We point out that its data-unobserved setup consequentially results in an incapability to generalize across different datasets as well as also high computational cost. This paper proposes a novel AutoFE framework Feature Set Data-Driven Search (FETCH), a pipeline mainly for feature generation and selection. Notably, FETCH is built on a brand-new data-driven MDP setup using the tabular dataset as the state fed into the policy network. Further, we posit that the crucial merit of FETCH is its transferability where the yielded policy network trained on a variety of datasets is indeed capable to enact feature engineering on unseen data, without requiring additional exploration. To the best of our knowledge, this is a pioneer attempt to build a tabular data pre-training paradigm via AutoFE. Extensive experiments show that FETCH systematically surpasses the current state-of-the-art AutoFE methods and validates the transferability of AutoFE pre-training.