No novel has ever answered the "big questions"
Is there a purpose to life? Why are we here? What is real happiness?
Plenty of novels have asked these questions, and all have ended without providing a definitive answer because these kinds of existential questions don't have an answer.
What authors do instead is explore the idea through an evolving situation or a character with a narrative arc, and the story concludes when the situation is resolved and the character has closure. Leaving the big questions unanswered is fine, so long as the reader doesn't feel they were taken on a sleigh ride to nowhere.
There needs to be more going on in the narrative than just conspiracies
Orson Scott Card introduced the MICE quotient – Milieu, Idea, Character, Event. According to him, stories typically revolve around one of these, but most stories will contain elements of all of them.
Here's a very simple breakdown how your Cicada 3301 conspiracy might play out under MICE.
Milieu – Several mysterious forces are locked in an endless battle of [whatever]. While the war never ends, this particular battle does (win, lose, or draw). The story is finished when this particular battle (a microcosm of the war) is resolved.
Idea – There is a mystery on the internet. What could it be for? Who made it, and why? Most important, what happens to the people who solve the puzzle? The point of an Idea story is exploring the idea itself. The story concludes when the idea is "fleshed out" even if the why and who is left unanswered. It's the idea of a web mystery that is interesting. A main character might not even be involved directly, he might be a journalist or armchair detective who becomes aware of the mystery, and begins to connect the dots. In an Idea story, the protagonist could be detached from the conflict like a psychiatrist, scientist, or archeologist. They are piecing together the "truth" behind the idea, or the idea itself changes how they see the world.
Character – The story revolves around a character who's story arc is about what happens to him (emotionally, psychologically) when he pursues this mystery. He meets strange people, he begins to fear for his life – the mystery triggers something within him that he can't let go and it ruins his marriage. Despite the apparent danger he becomes obsessed and is willing to risk everything. Character stories are finished when the character's arc is resolved. Again he may never understand the mystery, but he will come to the end of his arc.
Event – The event story is fixed around an inciting event, or an anticipated event. There may not be a central character, instead there are numerous characters reacting to the event. In this case the event might be the appearance of the online mystery, followed by other anticipated events like the reveal of more clues, or individuals solving bits of the mystery. Natural disasters and alien invasions are events that interrupt regular people's lives, potentially changing them forever. If the event happens early, the conclusion might be when the aftermath is finished (flood waters begin to recede, the crisis is over). When the event is at the climax it might be more like toppling dominoes that have been carefully laid throughout the story.
MICE is just one way to look at stories, but it's a useful one because it tells the author what sort of conflicts and resolutions are needed to keep the reader engaged. Readers inherently understand that although the "big picture" is about one thing, the story beats and character arcs – which are the actual narrative – will be in service to the type of story being written.
The "big picture" conspiracy doesn't need to be solved, but the immediate conflicts and narrative arcs come to their own conclusion.
Don't imitate bad episodic television
There are plenty of TV shows that had their 15 minutes of fame as the watercoolor topic of the day, but eventually collapsed under the weight of their own lingering unresolved nonsense. Lost, X-Files, and Altered Carbon all fall apart when viewed as a whole, but are able to keep viewers tuning in – for a while at least – just by presenting expensively-produced confusion and surprises. But don't mistake endless "wtf" plot-twists and pseudo-detective melodrama for "good" intrigue. Eventually even die-hard fans expect a payoff and a conclusion, not a shaggy dog story that goes on too long without a punchline.