Improving cell infiltration into engineered scaffolds and decelluarized tissue is needed for developing new and effective technologies in regenerative medicine and tissue engineering. Significant challenges associated with populating these structures with cells have persisted for many years. Here we describe a 3D bioprinting method for creating precise structures from natural extracellular matrix at low concentrations that facilitates cell infiltration after printing. We show that when printing collagen-1 solutions into a support medium made from jammed microgels, the printer’s basic operating parameters can be used to predict the resulting feature size. Microscopic examination of the printed features show that the collagen solution undergoes gelation and forms a network with the microgels excluded from the printed region. Using this method we 3D print a centimeter-scale model of a developing gut tube and we also show that cells are able to infiltrate printed collagen-1 structures. Our results demonstrate that a diversity of new approaches are possible for creating heterogeneously populated engineered tissue structures.