Rick explains that the parasites survive and multiply by implanting fake memories into the heads of others. We do not know if these parasites are in hiding, microscopic, or otherwise before they appear as physical manifestations; this is never explained, so we must make a few assumptions.
The first parasite the audience is introduced to is "Uncle Steve", who is quickly dealt with. Since we are only shown non-parasitic characters until after the title sequence, we must infer that at least 1+ parasites are in hiding, waiting for an open cue to integrate themselves.
Due to the mechanics of the false memories, it is also possible any family member had already met 1+ parasites prior to breakfast with "Uncle Steve", and is treating that encounter as natural, with the physical parasite hiding in a different room, waiting for an introduction to the audience later in the episode.
The second parasite the audience is introduced to is "Cousin Nicky"; he is created by Mr. Poopybutthole; this suggests that Mr. Poopybutthole is infected, and implies he may have encountered "Cousin Nicky" before breakfast with "Uncle Steve". "Cousin Nicky" is dispatched before another parasite appears. "Mr. Beauregard" appears next, followed by dozens of others.
As their method of genesis and disinfection is never explained, it is possible that any given parasite that appears is the first, and earlier parasites simply took the lead. It can be inferred that "Uncle Steve" was first, and not being disinfected, the family either then generated "Cousin Nicky", or "Cousin Nicky" (and subsequently "Mr. Beauregard") were in hiding, waiting to be introduced.
Truly, within the presented context of the episode, it is not possible to determine exactly which parasite was the "original", or even who brought the parasites into the house.