An exciting promise of quantum simulators is to enable a first-principles look into the real-time dynamics of matter after high-energy collisions of hadrons and nuclei, which mimic conditions in the early universe. To realize such a promise, first the gauge theories of the Standard Model should be mapped to quantum simulators. Then complex initial states, in the form of moving wave packets of composite (bound) states of elementary constituents, need to be prepared. While much progress has happened in the former in recent years, developments in the latter are just starting to gain momentum. In this talk, I will provide three examples from our recent work to demonstrate concrete proposals and algorithms for hadronic wave-packet preparations in confining models, from Ising spin systems to the low-dimensional Abelian lattice gauge theories. These examples involve a range of platforms, from (solid-state and atomic) analog quantum simulators to digital quantum computers. I will further present results for numerical studies of expected scattering outcomes, and conditions for observing inelastic channels, along with a demonstration of a high-fidelity meson wave packet generated on a trapped-ion quantum computer.