In this paper we study the Widom-Rowlinson model on a finite two-dimensional box subject to a stochastic dynamics in which particles are randomly created and annihilated inside the box according to an infinite reservoir with a given chemical potential. The particles are viewed as points carrying disks and the energy of a particle configuration is equal to minus the volume of the total overlap of the disks. Consequently, the interaction between the particles is attractive. We are interested in the metastable behaviour of the system at low temperature when the chemical potential is supercritical. In particular, we start with the empty box and are interested in the first time when the box is fully covered by disks. In order to achieve the transition from empty to full, the system needs to create a sufficiently large droplet, called critical droplet, which triggers the crossover. We compute the distribution of the crossover time, identify the size and the shape of the critical droplet, and investigate how the system behaves on its way from empty to full. This is a joint work in progress with F. den Hollander, S. Jansen, R. Kotecky.