A semiconductor device assembly includes a substrate and a semiconductor die adjacent to a first surface of the substrate. The substrate also includes a second surface opposite from the first surface, an opening extending from the first surface and the second surface, contact pads on the second surface, and substrate pads on the second surface, adjacent to the opening. Bond pads of the semiconductor die are aligned with the opening through the substrate. Intermediate conductive elements, such as bond wires, extend from bond pads of the semiconductor die, through the opening, to substrate pads on the opposite, second surface of the substrate. An encapsulant, which fills the opening and covers the intermediate conductive elements, protrudes beyond a plane in which the second surface of the substrate is located. Discrete conductive elements, such as solder balls, may protrude from the contact pads of the substrate to connect the semiconductor device assembly to another component, such as a printed circuit board or another packaged semiconductor device.