Consider the relativistic compressible Euler equations on flat Minkowski background. It is known that in low dimensions the homogeneous static solution is unstable: small perturbations lead to shock formation in finite time. In fact, for ϵ-sized perturbations, we also know that it takes at least 1/ϵ time for the shock formation to form. We ask the question: what happens when the background is curved and the universe only has finite amount of (proper) time left? A more precise version is: starting with a homogeneous big-bang solution to the Einstein-Euler system, what happens if we propagate (towards the big bang) a small disturbance? Is the big-bang singularity stable? Or do we hit a shock singularity first? We provide a partial answer to this question. This is joint work with Shih-Fang Yeh, and is partly contained in his PhD thesis.