Fractional quantum Hall systems are among the most exciting strongly correlated systems. Accessing them microscopically via quantum simulations with ultracold atoms would be an important achievement toward a better understanding of this strongly correlated state of matter. A promising approach is to confine a small number of bosonic atoms in a quasi-two-dimensional rotating trap, which mimics the magnetic field. For rotation frequencies close to the in-plane trapping frequency, the ground state is predicted to be a bosonic analog of the Laughlin state. Here, we study the problem of the adiabatic preparation of the Laughlin state by ramping the rotation frequency and controlling the ellipticity of the trapping potential. By employing adapted ramping speeds for rotation frequency and ellipticity, and large trap deformations, we improve the preparation time for high-fidelity Laughlin states by a factor of ten in comparison to previous studies. With this improvement of the adiabatic protocol the Laughlin state can be prepared with current experimental technology.