The aorist of γιγνωσκω, i.e., εγνων, is essentially a -μι (“athematic”) aorist. The participle is analogous to the aorist active participle of διδωμι, i.e., δους, from δο-ντ-ς, where -ντ- has dropped out before -ς, with the compensatory lengthening (Erzatzdehnung, as Timothée would say) of -ο- to -ου-. Similarly, γνο-ντ-ς > γνους. (Actually, the process was probably -ο-ντ-ς > -ο-ν-ς > ους.)
Unlike the aorist indicative active of διδωμι, the aorist indicative active of γιγνωσκω has a long vowel in the 1st, 2d and 3rd person plural (εγνωμεν, etc.). Usually, athematic verbs have short vowels in the indicative plural (εδομεν etc.), but εστην/εστημεν is an exception, as is εγνωμεν. In the case of εγνωμεν, this is possibly the effect of analogy, which tends to levelize irregularities in Greek as in other languages. (The explanation for εστημεν seems to go back deeper into the Proto-Indo-European prehistory of the Greek language.)
The present and aorist of the verb γιγνωσκω were presumably formed by two different processes from a primitive root γνω-/γνο-: (1) the present with the suffix -σκω + reduplication (which frequently accompanies the suffix -σκω), and (2) an athematic aorist. Most verbs, of course, are less “irregular”, but older, more basic verbs tend to exhibit “irregularities” like this.
It’s probably best not to think of this as an irregular process for forming the aorist. Rather, there is a “menu” of processes for forming each of the present, aorist, perfect and aorist passive/intransitive stems, and Greek verbs, especially older ones, often mix and match from these menus.
Hope this helps!