Now, assuming OP is "culture" and not "civilization", following is one really broad strokes take on looking at the question: Is domestication of plants an inevitably, or is it constrained by the availability of suitable candidate crops and climate?
The GGS style theory is that you really need the right candidate founder crops and animals around, and this is really part of the trigger that set off the Neolithic Revolutions where and when they happened. The converse is that early farming really could've happened anywhere, with almost any set of plants outside deserts, and really the triggers are something else.
If it's the former, and domesticates are important, then in theory an ASB world where these plants simply didn't exist would still I would guess tend to show the slow but steady increases in hunter gatherer toolkit complexity and sophistication which seem to happen on the average over time among populations across essentially every continent post-OOA (e.g. the Broad Spectrum Revolution), but never become sedentary or semi-sedentary agriculturalists. You'd might see composite bows, metallurgical exploitation, etc. without ever seeing agriculture, if you waited long enough (especially, as other people note, at particularly rich grounds for forager exploitation).
That's harder to achieve if it was an "almost any plant will do... but humans need to go through the right climatic events" scenario (for instance the Cold Snap scenario Spencer Wells lays out here -
https://blog.insito.me/the-neolithic-revolution-28a018799851). Though even in that case, agriculture can be avoided while maintaining increases in technology / sophistication, if you allow butterflying away of our climatic shifts.
Where it can't be avoided is if agriculture is simply an inevitable consequence of increases in human group size and the quality of the human toolkit, almost any plants will do, and no specific climatic shift was required. In that case, sophistication of HG cultures is probably capped to those that it was capped at in our world, in that once the toolkit becomes sophisticated to a certain level, and this happens outside extremely inhospitable cold and hot deserts, then agriculture becomes really inevitable.
(The same applies for animals and stock raising, though in that case, I would say it seems a good bit more tenable that particular animals were required, as the ubiquity of animal domestication is much less...)