Cells adapt and move due to chemical, physical, and mechanical cues from their microenvironment. It is therefore important to create materials that mimic human tissue physiology by surface chemistry, architecture, and dimensionality to control cells in biomedical settings. The impact of the environmental architecture is particularly relevant in the context of cancer cell metastasis, where cells migrate through small constrictions in their microenvironment to invade surrounding tissues. Here, a synthetic hydrogel scaffold with an interconnected, random, 3D microchannel network is presented that is functionalized with collagen to promote cell adhesion. It is shown that cancer cells can invade such scaffolds within days, and both the microarchitecture and stiffness of the hydrogel modulate cell invasion and nuclear dynamics of the cells. Specifically, it is found that cell migration through the microchannels is a function of hydrogel stiffness. In addition to this, it is shown that the hydrogel stiffness and confinement, influence the occurrence of nuclear envelope ruptures of cells. The tunable hydrogel microarchitecture and stiffness thus provide a novel tool to investigate cancer cell invasion as a function of the 3D microenvironment. Furthermore, the material provides a promising strategy to control cell positioning, migration, and cellular function in biological applications, such as tissue engineering.