As a glass-forming liquid is cooled, the dynamics of its constituent particles changes from being liquid-like to more solid-like. The solidity of the resulting glassy material is believed to be due to a cage-formation process, whereby the motion of individual particles is increasingly constrained by neighbouring particles. This process begins at the temperature (or particle density) at which the glass-forming liquid first shows signs of glassy dynamics; however, the details of how the cages form remain unclear(1-4). Here we study cage formation at the particle level in a two-dimensional colloidal suspension (a glass-forming liquid). We use focused lasers to perturb the suspension at the particle level and monitor the nonlinear dynamic response of the system using video microscopy. All observables that we consider respond non-monotonically as a function of the particle density, peaking at the density at which glassy dynamics is first observed. We identify this maximum response as being due to cage formation, quantified by the appearance of domains in which particles move in a cooperative manner. As the particle density increases further, these local domains become increasingly rigid and dominate the macroscale particle dynamics. This microscale rheological deformation approach demonstrates that cage formation in glass-forming liquids is directly related to the merging of such domains, and reveals the first step in the transformation of liquids to glassy materials(1,5). The onset of rigidity in a two-dimensional colloidal glass-forming system is identified by the formation and merging of locally rigid domains in which particles move in a cooperative manner.