General relativity and its highly successful geometric description of gravity are among the greatest scientific achievements. However, geometry may not be the true physical nature of gravity. Understanding the possible non-geometrical nature of gravity could lead to its inclusion in the Standard Model of particles and fields, as well as its quantisation. From this perspective, we propose the group, consisting of two interacting sectors ( and ), as the simplest possible Toy Model for unifying the strong and gravitational forces. According to the mathematics of the unification, the gravitational charge of gravity should be the trace of the Energy-Momentum tensor, which is a Lorentz invariant. Since gravity is long-range and nonlinear, the corresponding gauge boson must be massless and possess a non-zero gravitational charge, . This is impossible in classical field theory, in which . The gravitational charge is possible only in quantum field theory due to the quantum vacuum and trace anomaly phenomenon. According to , therefore, gravity is a purely quantum phenomenon: the gravity we know is the macroscopic manifestation of the quantum trace anomaly (i.e. more generally, of the quantum vacuum). Another crucial consequence is the transformation of the quantum vacuum into a topological fluid consisting of topological gravitational dipoles, among other things. This calls for a rethink of everything, from the cosmological constant problem to dark matter and dark energy and could potentially solve at least some of these problems. It could also provide an alternative explanation for phenomena such as light deflection and perihelion precession. The unique goal of this conceptual paper is to promote this emerging field of fundamental research. Detailed analyses will be provided in a series of forthcoming papers.