Abstract: Little is known about the expansion history of the universe before 5 MeV. A period of early matter domination (EMD) arises naturally in models with weakly coupled axion-like particles (ALPs), driven by the radial partner of the axion. EMD also allows high-scale ALPs to achieve the correct relic density without fine-tuning of initial conditions and can substantially modify structure formation, increasing power on small scales. We estimate the properties of ALP miniclusters in these models and discuss some of their implications for experiment.