Solitons can form bound states that are frequently referred to as soliton molecules as they exhibit molecule‐like dynamics. The build‐up phase of the optical soliton molecule remains elusive. Here, by means of a time‐stretch technique that enables real‐time access to the spectral and temporal dynamics, rich nonlinear processes involved in the build‐up of soliton molecules are revealed in an ultrafast fibre laser. Specifically, the formation of closely‐ and well‐separated bound solitons are resolved. In both cases, the build‐up phases consist of three nonlinear stages including mode locking, soliton splitting, and soliton interactions. For closely‐separated bound solitons, soliton interactions display wide diversities in repeated measurements, including soliton attraction, repelling, collision, vibration, and annihilation. For well‐separated bound solitons, repulsive interactions dominate the soliton interactions. Numerical simulations corroborate these experimental observations. Furthermore, a conceptually different soliton molecule, the intermittent‐vibration soliton molecule, is discovered and characterized. It is the intermediate state between the vibrational and stationary soliton molecules. The author's findings could assist in the understanding of the build‐up phase of localized structures in different dissipative systems.