One way I've done this is to start with the middle. Start with something one character knows and the other does not, and figure out the consequences.
Once you figure out how the characters would respond to something, you can either figure out what in their backgrounds have caused this, and/or figure out what they would have tried to do or would do next.
If they don't want to tell people what they know, they have to have a reason. This means that you can flesh out the beginning of your story explaining why. Chances are, you'll introduce other characters who influenced them (possibly in ways no character planned). These characters will have plots of their own.
If they can't tell people, that means something is stopping them. This means that there's another character/entity acting. Figure out why they would do that. This also fills in the beginning.
Now, once you have some of the beginning, you can go forward and figure out what all of these people would do. Then, once you've gotten as far as you can with that, of if you figure out that you need more external factors, repeat this process.
For instance, here's roughly one train of thought for part of a sifi story I have been meaning to write down for a while.
First thoughts: Background character O is a doctor, who figured out the cure for a plague, but doesn't like the spotlight. Another character, call her J, is a genetically engineered alien, because cool factor of putting those words together. Also, there's something about the cure that O can't tell anyone about; let's focus on that because I don't want to go too into technical details.
So far, this is very thin. One character has a premise which is basically, "cool genetic things," another is a "reclusive genius" archetype defined entirely by work I'm going to refuse to specifically talk about.
Okay, where do I go from there?
J is a genetically engineered alien, what if that alien species that created her genetically engineered the plague as a weapon?
That has implications. Since the plague was devastating, that would imply that humanity would be seriously outmatched in a conflict.
But the intentionality could lead O to want revenge. That's an additional motivation for her, which is directly in conflict with her Hippocratic oath. Or is it? Does she think of the oath as human-specific? Let's say O's not deterred from revenge. That probably means that she's at least slightly xenophobic.
I had vague plans for other alien species--what if humanity isn't the first species these aliens have attacked with a plague? What if the cure O found came from adapting one they found? What if the hostile aliens don't want anyone else cooperating to take them down? That would explain at least additional reason why O wouldn't want the spotlight. Then it could be a matter of "you don't know we know." ... This is the definition of a conspiracy. Fun! But also what was the effect of plagues on their societies?
O getting revenge would then also be hampered by needing to prevent an inter-species war that humanity would loose badly. That also means she would act mostly alone and not shout what she knows from the rooftops. What would she prioritize? Let's say revenge at first.
So, what would O do to get revenge? Probably leave being an active doctor/researcher. Okay, that gives her an excuse to tag along with the main characters. Perfect! That means that the other main characters would have to be at least kinda unconcerned with rules, because she probably wouldn't want to work strictly within what was perfectly legal for a revenge mission. I'll work that into the rest of their stories.
This would mean that O would be in direct contact with J, who is with the main characters/one of the main characters. Biology is hard, so would J be well-adapted? And if O was there, wouldn't O be J's doctor? This is an opportunity for further character development for O. The two would probably have a lot of contact where J was simply uncomfortable and very non-threatening. What if O starts to view aliens as people too?
Sure she wants revenge, but what specifically did O lose during the plague? Since she is willing to risk everything to get revenge, she probably doesn't have many people she cares about. She probably had a family at one point; okay, they're dead now. Is the memory of the loss worth more to her than her possibly-developing friendship with J and with the other characters? Changing her mind about that could be the turning point in her story.
Does J know what happened? Let's say yes and no, yes but not all of it. What does that mean for her?
Very rarely is there a lone genius like Salk making a development. But I want this. That means that there was some serious mortality in the medical field, and that she's the only one who survived long enough to work on it. (Makes sense, considering what happened with the Black Death.) Okay. Why would O be immune? Back to backstory. Since it was genetically engineered, there might be an already-created vaccine created by the aliens. Why would she have been given that? This means further development for the aliens.
Why did the aliens make the plague in the first place? I don't want them to be cartoonish villains, doing evil for the evil. This means that they must have been threatened by something that humanity is doing. Did the plague succeed in its objective? Let's say no. Okay, what was that? What are they doing now? Is this related to why J is in the story?
And so on. This is abbreviated, but I think it illustrates the method. From a handful of somewhat varied character ideas, using this method of iterated development, I've managed to come up with a plot that I can't easily explain to anyone in under an hour, with at least five different government actors, upwards of twenty important characters all with their own individual arcs, three main plots, and multiple conspiracies, spanning a bit over 200 years. (Very little of which is described here.)
Caveats: I've been working on this particular story for about 4 years, on and off, and haven't written much of it down, though I have written down others I've structured using this method (this was just the first example that came to mind). Also, if you work at it long enough, you will probably find characters changing their motivations over time, particularly for the characters you didn't focus on at the beginning. (Additionally, you may find that the most natural place to start will be in medias res.)
In the stories I've written down, I have had to go back to the beginning chapters to update setting things I figured out later. But I think that might be inevitable if you're a discovery writer?
That said, I think this method is pretty effective at creating interesting plot, and it definitely doesn't require knowing anything about how it's going to end at the beginning.