Thanks @DMGregory for the pointer in the comments.
I'm constructing a fullscreen quad at (x, y, -1, 1) in NDC. Notice z = -1 is the near plane in NDC (left-handed unlike normal coordinate systems in OpenGL-land).
In the vertex shader:
attribute vec2 aVertexPosition;
uniform mat4 uInvViewMatrix;
uniform mat4 uInvProjMatrix;
varying vec3 vZNearPos;