"We" (Homo sapiens) did not invent fire. Our predecessor species were already using it.
Firestarting is harder to pin down and may be within the scope of homo evolution.
<https://en.wikipedia.org/wiki/Control_of_fire_by_early_human...>
Ever since Earth’s atmosphere had sufficient oxygen to sustain fire given a fuel source and heat, fire has exists.
If we can lay the blame on anyone for having started fire it’s going to be whoever fine tuned the constants such that there is anything here at all.
1. Language already emerged with early hominins (paranthropus and such).
2. Habilis et al developed toolmaking to a level that carrying stuff around was of critical importance.
3. H. erectus emerged from walking, and brought technology to a "civilized" level.
4. Anything post erectus evolved for civilized society.
5. The destruction of soils in eurasia about 24000 BC
6. The destruction of soils in the Americas about 9500 BC
7. Old metallurgy age.
8. Tin bronze age.
9. Recorded history.