Summary: We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on \(\mathbb{Z}\) starting from an arbitrary initial profile. We generalize earlier works by T. Seppäläinen [Ann. Probab. 27, No. 1, 361–415 (1999; Zbl 0947.60088)] and E. Andjel et al. [Stochastic Processes Appl. 113, No. 2, 217–233 (2004; Zbl 1080.60089)]. Our constructive approach requires new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our setting.