Why does ignorance (avijjā) appear as the first link in the chain of dependent origination?

The Dependent Origination cycle is the cycle of (i) birth, (ii) death & (iii) suffering, which means the mind suffering over the (actual or imagined) death of loved ones/things. The word 'death' ('marana') in Dependent Origination means 'death of a self' or 'death' of ignorance constructed 'existent beings'. SN 12.2 says:

The passing away of the various beings from the various orders [classifications] of beings, their perishing, breakup, disappearance, mortality, death, completion of time, the breakup of the aggregates, the laying down of the carcass: this is called death.

SN 12.2

SN 23.2 says 'a being' is a state of strong clinging:

'A being,' it's said. To what extent is one said to be 'a being'?"

"Any desire, passion, delight, or craving for form, Radha: when one is caught up there, tied up there, one is said to be 'a being.'

"Any desire, passion, delight, or craving for feeling... perception... fabrications...

"Any desire, passion, delight, or craving for consciousness, Radha: when one is caught up there, tied up there, one is said to be 'a being.'

SN 23.2

As for ignorance, the Pali is 'a-vijja', which means 'non-realisation' or a 'lack of true knowledge'.

Ignorance is the most pervasive of seven underlying tendencies all people have at childbirth; which is why it is listed last as one of the seven underlying tendencies and why it is the last of the ten fetters to be broken for full enlightenment. Thus the teachings say ignorance is the leader/forerunner (pubbaṅgamā) of all unskilful mental states (SN 45.1).

The teachings also say no beginning point or prior cause of ignorance can be found (AN 10.61); that the only condition for ignorance that can be found are the five hindrances, which are the food/nutriment ('ahara') that maintain the pre-existing ignorance. The five hindrance, which maintain ignorance, i.e., prevent the arising of insight knowledge, are (i) sensual desire, (ii) ill-will, (iii) sloth & torpor, (iv) restlessness & remorse and (v) doubt.

MN 9 offers a similar explanation to AN 10.61, when saying:

And what is ignorance? Any lack of knowledge with reference to suffering, any lack of knowledge with reference to the origination of suffering, any lack of knowledge with reference to the cessation of suffering, any lack of knowledge with reference to the way of practice leading to the cessation of suffering. This is called ignorance. From the origination of fermentation (asava) comes the origination of ignorance.

There are these three fermentations: the fermentation of sensuality, the fermentation of (self) becoming, the fermentation of ignorance. This is called fermentation. From the origination of ignorance comes the origination of fermentation.

MN 9

It follows, not only does ignorance inherently exist, but the underlying tendencies that continuously flow out of the mind, rooted in sensual & self-becoming drives, block the development of true knowledge.

In conclusion, ignorance is the first condition of Dependent Origination because it represents all of the seven underlying tendencies which flow out as the three asava (fermentations), of which it the most pervasive one of each.

If an individual knew how things worked to cause their suffering now, knew how to be released from their suffering, they would not suffer anymore, right? Ignorance of all that is what I mean.

why is ignorance placed at the very beginning of this chain?

Because if we didn’t ignore, we would have noted the presence of craving and what it is doing to our consciousness, perception, feeling and the accompanying mental formations i.e. our mind. Once our mind is tainted with cravings (for pleasant experience), our intentions are tainted (for pleasant experience, aversion at unpleasant ones and searching when encountering boredom) with their accompanying unskillful consequences. If we had noticed (instead of ignoring) the presence of craving, there would have been many opportunities to quench this thirst and avoided all the unwholesome results it brings once and for all.

Does this imply an absolute beginning in time, or is it pointing to a structural relationship in how suffering arises?

Where there is a cause, there is an effect. This implied that there should be a beginning but it is lost in antiquity. Besides, my beginning may not be the same as yours; just as yours is not necessarily the same as others. Likewise, one’s Nirvana (i.e. freedom from samsara) is not dependent on or synchronous with another’s and vice-versa. I believe the relationship with suffering is that it all began with this habit of ignoring (giving rise to ignorance). When did the mind pick up this bad habit of ignoring stuff and their consequences is irrelevant. In Buddhism, I believe what is important is to rid ourselves of it.

ignorance is simply a lack of knowledge, or if it refers to a deeper mis-perception of reality that underlies all conditioned experience

What makes ignorance (a state) scary is the habitual tendency to ignore (the action) that give rise to this state. A lack of knowledge in and of itself is unintentional. In karmic sense, an unintentional action carries no unskillful results. But if one intentionally ignores things that are happening and their potential harmful consequences to oneself and others due to carelessness, recklessness and heedlessness then that carries bad karmic consequences. Examples are ignoring consequences from vaping, lack of exercise, eating junk food and so on. Can we be certain there are no consequences to doing these things? No, but the mind habitually inclines towards ignoring whatever consequences that might exist because they represent inconvenient truths.

And like all karmic actions, there is also a habitual aspect to it i.e. there is a likelihood that we will keep repeating this same action (to ignore out of carelessness, recklessness and heedlessness) again in future and suffer its karmic consequences, simply because we don’t see the harm and danger of this habit.

Contrast this habitual tendency to ignore carelessly, recklessly and heedlessly with the constant mindfulness of an arahant in AN 7:63.

Just as the royal frontier fortress has a gatekeeper—wise, competent, intelligent—to keep out those he doesn’t know and to let in those he does, for the protection of those within and to ward off those without; in the same way a disciple of the noble ones is mindful, endowed with excellent proficiency in mindfulness, remembering & able to call to mind even things that were done & said long ago. With mindfulness as his gatekeeper, the disciple of the noble ones abandons what is unskillful, develops what is skillful, abandons what is blameworthy, develops what is blameless, and looks after himself with purity.

Notice that ignoring or being mindful are both habits (albeit with a mutually exclusive relationship). The difference is one habit had been with us since antiquity. The other is one that we would need to cultivate to full accomplishment in order to fulfill the Noble Eightfold Path.