We present Shamrock, a performance portable framework developed in C++17 with the SYCL programming standard, tailored for numerical astrophysics on Exascale architectures. The core of Shamrock is an accelerated parallel tree with negligible construction time, whose efficiency is based on binary algebra. The Smoothed Particle Hydrodynamics algorithm of the Phantom code is implemented in Shamrock. On-the-fly tree construction circumvents the necessity for extensive data communications. In tests displaying a uniform density with global timesteping with tens of billions of particles, Shamrock completes a single time step in a few seconds using over the thousand of GPUs of a super-computer. This corresponds to processing billions of particles per second, with tens of millions of particles per GPU. The parallel efficiency across the entire cluster is larger than $\sim 90\%$.