My Approach To Setting Up A Sandbox Campaign With Movement And Life Beyond Just The PCs

That said, here is how I deal with player agency and avoiding railroads: 

I start with a few major actors (bad, neutral, maybe a few good as far as the players go). I give these actors personalities, a bit of a past, a sense of how they pursue things they feel the need to, and any particular weaknesses they might have. 

I then look at what these major actors would do in the setting (at least at the start). Invade somewhere? Seek to gather resources? Hunt down and capture or kill some folk? Try to open a very long sealed and mostly unknown temple? Etc. 

I consider these major actors to likely have assets and figure a few fairly reasonable groups and their competence. I also think if their leaders might have any  axes to grind with the major actor that is using them. 

Once I have a handful of major actors, and their current projects, and then look to where that might occur (and some of it is bound to be near to the PCs). 

I then come up with a simple plan for these actors as to when and how they launch their projects.

So, how does that tie to the PCs?  Possibly:

* proximity to some minions acting

* hearing about an event

* someone deciding their brother might have been in one of the abductions (as an example)

* an NPC might have reason to speak to them on this matter

* or nothing at all

Over time, these different major actors are going to clash with the players probably (not 100%, but it seems likely) and with each other. 

Those actors agendas move forward (and there would be rolls for how successful if the PCs aren't there) and return to the point of planning for the next cycle. (and all major players may not be re-evaluating and pivoting on the same schedule)

Players would probably run into the major actors' minions in some way and may not even realize they are part of any sort of larger plan. The minions may have minions (repeatedly) to give cutouts and a structure for the players to deal with. 

You don't need big details for most of that - just a small file card of the people that are powerful or well enough to be known. Some of them may falter or pass or depart, new ones may arrive to the setting. 

In this respect, the fate of these plans (PC present or not) will have to be resolved. 

Each project step could draw the attention of the characters or run into the characters. 

In effect, there is a (computer analogy) a background process running for each major actor. There is resolution engine (a roll) to produce some outcomes maybe with some modifiers that may apply. Then that outcome leads into what's next. 

The players can, and likely will in the early part of the campaign, not see the larger actors and their goals. It may take multiple encounters and some finding of information (or some other smart way of discerning that there is something bigger going on and to search for who might be involved). 

The players, for their part, can be pursuing their own interests. If they don't impact the players (due to lack of proximity or knowledge or apathy), then its simple for the GM to take a few minutes each post-session to see what changed and how the actors might act (their actions will be randomized but with respect applied to their nature and goals and their limited knowledge of what is happening). (You only have 4-6 of these big actors at any  point). 

Players have all the agency, but things in the environment can come up that might draw them in. Or they might on their own jump in. Or they may let big events while smaller events have their attention. 

I don't like just encounters randomly popping up - it fails to consider the notion that some powerful NPCs would have a plan that they will be trying to push forward. I like the idea that there are key actors that are in motion even as the PCs are. 

It's possible the players may align with one (just because 'strong boss!') or as a way to get knowledge or to foment a clash between other major actors and their minions. But we don't know that... but there is some structure and action at the highest level that runs without the players unless the players wade into it somehow. 

Now, the PCs are likely, but not guaranteed, to engage in some actions that will yield the raw intel to figure out something bigger exists and is in action.  I kind of expect them to pursue such things, but I won't force them - their choice is unburdened (in 95% of times... sometimes you end up ambushed or in trouble so there is a degree of compulsion but it comes from the situation and actors, not really from GM desires). 

I find this way to let the major actors be active and engaged in their own agendas and the smaller folk (including the players at first) may be ignorant or not ready to pursue these larger issues). 

It's mostly sandbox, but a sandbox populated with some powerful people or entities with agendas and their decisions will be randomized, with % based on what would make sense for them  (sometimes several things so maybe they don't end up doing what I thought they would). 

You want the world to feel alive and moving. You want the layers to feel engaged in it but having the knowledge that their agency is prime. 

Also, just to be clear: Even writing a encounter table is an act of GM intervention. Even if all the possible outcomes of a D100 giving 100 outcomes is there, someone loaded the table. So there never quite 100% random things coming at the players. The scope is determined by the encounter size, type and intent. 

In that respect, I still think my method is effective in having motion in the world without stealing much from the player's agency. They also have to be the ones to figure out much of what is going on and what they want to do to address it. That's all them. And thus that's also theirs as far as end game and what it looks like - many, many possible ways.