The main character of my novel (third person limited) is an outlaw, on the run from government agents and living from day to day trying to survive.
In the first quarter of the story, she doesn't really have any sort of "end goal" that she is working towards outside of trying to remain free. She is just sort of carrying on surviving on her own, angry at the world and devoid of any solutions to her situation.
She eventually gets captured by the government, and has to work for them to obtain her freedom, but up until this point she has no long-term ambitions or desires outside of evading the law.
I feel like the beginning of the book is quite balanced between world-building, character development and actual interesting events happening, but the main character isn't working towards any specific objective, nor does she have any real idea of one.
My concern is that it will be difficult for readers to invest in a story about a character that doesn't really know what they want or where they are going. Obviously this changes later on, but my issue is that the reader may have put the book down before this change happens if they don't know what the book is about or working towards.
My understanding is that most novels (specifically in the sci-fi/ fantasy genre that I'm writing in) introduce very early in the story at least some sort of notion of an antagonist, a plot or an overall theme of "something is wrong and needs to change" that the protagonist will confront in the climax of their journey. This usually lets the reader know what to expect of the forthcoming story.
The point of my story and main character, however, is that they are completely separated from these things, living outside of society and minimizing contact with others, cutting herself off from the wider world.
So how can you convince readers to be invested in a story that initially has no recognizable trajectory? Or alternatively, how do you manufacture an end-solution for a character that doesn't really have any sort of direction?
You say "the first quarter of the story". That is close enough to ACT I, the setup, and it ends with a crisis that propels the character into ACT II, in your case, capture by the government. You are probably writing to the Three Act Structure instinctively; we absorb this by examples of the tens of thousands of commercial stories we listen to almost every night (TV, movies and books).
That's a good thing.
In the first Act, we establish the normal world of your hero; her day to day life. So it is okay if we begin with her normal world being on the run evading the law. You begin "in the middle" which is good, provides action, and makes your character reasonably competent and (hopefully) proactive in trying to escape.
The end of the first act ends in a turning point moment, when the characters life will never be the same, and a major failure is very common. It is not the only thing; a plane crash or other accident is common too, being victim of a crime is common. But her major failure of being captured, failing her goal of escape, is a good one.
And the rest of your story follows that: Eventually she does escape, by working for her freedom by completing her indentured servitude to the government. (Which I hope is very dangerous work.)
The solution to your problem is giving your character either false goals, or sub-goals, she is pursuing during Act I. Here is the synopsis of ACT I of Die Hard:
New York City policeman John McClane (Bruce Willis) is visiting his estranged wife (Bonnie Bedelia) and two daughters on Christmas Eve. He joins her at a holiday party in the headquarters of the Japanese-owned business she works for. But the festivities are interrupted by a group of terrorists who take over the exclusive high-rise, and everyone in it. Very soon McClane realizes that there's no one to save the hostages -- but him.
Note that McClane has a "false goal" in the beginning of his story, his marriage is on the rocks, he has daughters he has to go someplace to visit. This establishes he has something to lose if he doesn't fight, but otherwise has nothing to do with the main plot of the story, stopping ruthless terrorists. (Maybe we show them once in awhile to reinforce the stakes so he doesn't give up, I don't recall.) I believe in the end McClane's "false goal" of a better relationship with his wife and kids is achieved, by credit for his heroism.
Your fugitive does have a goal, a life of freedom, which seems interrupted but is ultimately achieved even though her life is changed. That is what you need to reinforce, that her goal is to escape and find a place where she won't be constantly on the run.
You do that with a series of Try-Fail cycles in the first Act.
- She tries one thing, it fails but she easily escapes. She learned something that leads her to another goal.
- She tries, it fails. The law has more men after her this time, and she narrowly escapes! That gave her a different idea.
- She tries. It fails, and the law has even more men and more competent in the bargain, and she narrowly misses escape. She is captured.
We escalate in these cycles; Escape was [Easy, Hard, Impossible]. The law men are [Few, Many, Overwhelming].
- Your villain in ACT I is The Government and law enforcement.
- Her goal is freedom, both from prison and pursuit.
You need to make her very good at something (which is why the government is willing to bend the rules and employ her instead of imprisoning her), and that needs to be on display in her exploits to escape and find some sanctuary. Being good at something is one component of a likable character; another is to not just be constantly reacting to problems, but find a way for her to initiate actions to solve them. She must have her own ideas and pursue them.