The Greek word genesis (γένεσις) has the root gen, but where does the suffix -esis come from?

Γένεσις /ɡénesis/ “Genesis, origin” consists of the verb root gen- “to originate”, and the ending -esis.

The -εσις ending of Greek genesis has two components. The –sis component is a nominalisation, indicating the result of a verb. Cf. ly-sis ‘solution’ < lyō ‘solve’; gennē-sis ‘birth’ < gennaō ‘give birth’; pep-sis ‘digestion’ < peptō ‘digest’; theōsis ‘becoming God’ < theoō ‘make a God’.

The vowel before the –sis, if any, depends on the conjugation of the verb.

• A normal thematic verb (with a thematic vowel connecting inflections to the verb stem) does not use a vowel: ly-sis; pep-sis < *pept-sis.
• A contracted thematic verb (verb stem already ends in a vowel) often lengthens the vowel: the-ō-sis < the-o-ō; genn-ē-sis, Doric genn-ā-sis < genn-a-ō.
• A contracted thematic verb in –eō may or may not lengthen the e; this usually correlates with whether the e is lengthened in the aorist passive. blasteō ‘to sprout’, aor.pass. eblastē-thēn, blastē-sis ‘sprouting’; haireō ‘to choose’, aor.pass. haire-thēn, haire-sis ‘choice’.
• An athematic verb (with no thematic vowel: an archaic class of verbs) has a short vowel before the ending. hi-stē-mi ‘stand’, Doric hi-stā-mi > sta-sis. di-dō-mi ‘give’ > do-sis. ti-thē-mi ‘put’ > thesis.

And here I get stuck, I’m afraid. I can’t work out why the vowel in genesis is an epsilon instead of a zero, *gen-sis > *gessis, or an a which corresponded to the Indo-European schwa, cf. teinō ‘stretch’ > tn-sis > ta-sis ‘tension’. I think somehow this is a pattern with second aorists, e-gen-omēn ‘I became’ > gene-sis ~ e-sch-omēn ‘I was had’ > sche-sis ‘relation’.

But in any case: the vowel is not part of the suffix, but a connector.

EDIT: the actual answer is Neeraj Mathur’s answer to The Greek word genesis (γένεσις) has the root gen, but where does the suffix -esis come from? I’m leaving this up because it takes you halfway there, and Neeraj resolves the -e- issue where I got stuck; and this is good information to know for less archaic verbs anyway.