The breakdown process in gases is a versatile research topic. Numerous processes play more or less important roles in discharge formation, strongly depending on the gas mixture, the electrode configuration, the applied electric field, the size of the geometry, and even on the structures surrounding the active volume where the breakdown takes place. We focus our research on the breakdown process in argon at 700 mbar, in a pin–pin (point-to-point) electrode geometry, with increasing positive voltage at the active electrode. The voltage rises by 100 V/ns. We use a 2-D fluid model to examine the formation of a charged channel between the electrodes under given conditions. We find that the results describe previous experiments reasonably well. We also explore the role of excited argon atoms at $(4s)$ metastable levels in the breakdown process, and we conclude that the ionization path with an intermediate step containing the metastables does indeed make a notable difference in the breakdown process.