The oscillating onset of the Rayleigh–Bénard convection with viscoelastic fluids in a slightly tilted two-dimensional rectangular cavity with an aspect ratio of Γ = 2 was investigated for the first time via direct numerical simulation. A series of simulations were conducted in the plane of the Rayleigh number ( Ra) and the tilt angle ([Formula: see text]) with three Weissenberg numbers [[Formula: see text]] at a fixed Prandtl number Pr = 7.0. The evolutionary path of the oscillating convection onset in the [Formula: see text]-plane was determined, and the corresponding complex flow structures were observed. The inclination of the box delays the onset of the oscillations and the corresponding Rayleigh number Rac as compared to the horizontal configuration. Oscillating flow structures acquire the attributes of a traveling wave. A specific feature of the oscillating convection in the case of the horizontal cavity is that the periodicity in space and time exists in the inclined box case as well. However, the evolution of the oscillatory flow structure is very different from the horizontal case in that the counterclockwise cell assimilates the clockwise cell [Zheng et al., “Pattern selection in Rayleigh–Bénard convection with nonlinear viscoelastic fluids,” Phys. Rev. Fluids 7, 023301 (2022)].