Automating the assembly of objects from their parts is a complex problem with innumerable applications in manufacturing, maintenance, and recycling. Unlike existing research, which is limited to target segmentation, pose regression, or using fixed target blueprints, our work presents a holistic multi-level framework for part assembly planning consisting of part assembly sequence inference, part motion planning, and robot contact optimization. We present the Part Assembly Sequence Transformer (PAST) -- a sequence-to-sequence neural network -- to infer assembly sequences recursively from a target blueprint. We then use a motion planner and optimization to generate part movements and contacts. To train PAST, we introduce D4PAS: a large-scale Dataset for Part Assembly Sequences (D4PAS) consisting of physically valid sequences for industrial objects. Experimental results show that our approach generalizes better than prior methods while needing significantly less computational time for inference.