Verb for doing something unknowingly

There aren't many concise verbs to describe what you are wanting. I would suggest rephrasing to use an Adverb, such as: Inadvertently

A moment later, nevertheless, McChrystal may have inadvertently revealed what motivated the entire coverup.

Dictionary.com

They are muddling into a materialistic society.

From http://dictionary.reference.com/browse/muddle:

7. to behave, proceed, or think in a confused or aimless fashion or with an air of improvisation: Some people just muddle along, waiting for their big break.

gravitate to or towards (verb):

1. Move towards or be attracted to a person or thing

'young Western Europeans will gravitate towards Berlin'

2. (Physics) Move, or tend to move, towards a centre of gravity or other attractive force

'the moon gravitates towards the earth'

3. (archaic) Descend or sink by the force of gravity

'water gravitates towards the sea; vapour rises to the sky'

Source: ODO

The example sentence, above, becomes:

'S/he gravitated towards a materialistic society.'

He is sleepwalking into disaster.

To submit? or perhaps to resign?

In the exact sentence you've given as an example, I'd use slump

Slump: to move down or forward suddenly

Slump: a marked or sustained decline especially in economic activity or prices

Humanity slumped into a materialistic society

It gives the impression of an untended stack of stuff that just randomly toppled into a mess one day.

If you want something more active, you might try bumble.

Bumble: to proceed unsteadily

Humanity bumbled into a materialistic society

When used in your sentence, that should give the impression of a lot of seemingly undirected movement resulting in the transition you describe.

In both cases, the phrases would indicate that society did what you ascribe to them without consciously deciding to do so; that it was asleep at the wheel, so to speak. Slump implies an almost callous disinterest as a causal connotation, while bumble implies ineptitude.

You might also choose blunder, stumble or fumble as fine synonyms for bumble in this case.

For slump, you could also consider slouch, as in the title of the book "slouching towards Bethlehem", a collection of essays which together depict the sort of "arrival due to aimless wandering" I think you're looking for.

Evolve fits your needs and in particular your example pretty closely. Evolution is a natural process, implying the lack of intention you're looking for. It also fits your example as it's an act of change and development.

Similarly, you might consider mutate, another natural occurrence with greater emphasis on randomness and less emphasis on a direction of development.

More generally, you could say my answer is: use a context-specific verb which emphasizes nature (i.e. the lack of human intention) as the driving force behind the action.

How about "to find oneself" [doing something], to indicate that all of a sudden someone realizes she's in a circumstance she hadn't expected to be in:

2). (idiomatic) To unexpectedly or unintentionally begin to do or experience something.
When news of his wife's murder spread around the media, he found himself in front of a press conference explaining his actions.

Wiktionary

How about “subconsciously” walking, sliding, etc. “into materialistic society”?

The subconsciously (adverb) part allows for the passive and active aspects of “doing something unknowingly yet doing it nonetheless.”

sub·con·scious·ly.
adverb: subconsciously; adverb: sub-consciously in a way that is influenced by the part of the mind of which one is not fully aware. "maybe subconsciously I was trying to sabotage the deal" (from online search under “subconsciously.”)