A packaging machine is for forming a product cavity in a web including a forming die box defining a recess into which the product cavity is formed. An insert is axially movable in the recess to thereby vary a depth of the recess. A variable depth mechanism selectively moves the insert to vary the depth of the recess. The packaging machine includes a latching mechanism that moves the forming die box into and between a first position in which the forming die box is spaced apart from the die box base and a second position in which the forming die box is supported by the die box base.