Lil Cal has been identified as a juju, and as such, his existence is an ontological paradox, meaning he has no true point of origin.
Cal is first introduced as having been part of Dave's upbringing by his bro; however it quickly becomes apparent that Dave is severely unnerved by the puppet. This turns out to be partly due to the presence of a copy of Cal in Dave's dream room on Derse's moon. The existence of this version of Cal is not explained at this point in the story, and was assumed to simply be a consequence of Dave's exposure to Cal while awake.
Once the session begins, other characters become entangled in Cal's circuitous path through paradox space. During a visit to Dave's dream room, dream Rose becomes annoyed by Cal and throws him out of the tower. Rather than plummeting to an uncertain fate, Cal miraculously lands on Bro's traveling hoverboard, which brings the puppet to the ectobiology lab in the Veil through a transportalizer. It is assumed that, shortly after, when the other Guardians were preparing for the ectobiology session to begin, Dave's Bro gave Cal his signature gray hat. During the events of The Reckoning, dream Cal is then assigned to a meteor with baby Dirk, who later grows into Dave's bro. This means that the real Cal who torments Dave in his waking hours is, in fact, a future version of the very same Cal who haunts his dreams.