But if you don't give them some kind of prompt.....a map found in a treasure hoard, a rumor heard in an inn, a reward poster on a community board......absent those kinds of prompts, how do your players know what to engage with? Are they that familiar with your setting that they can simply set their own agenda?
Everyone's talking about "players get to do whatever they want" so I'm trying to understand how those wants might develop.
I can give you a bit of an idea of how things fell out in my 1st 4e campaign. This game was very evolutionary for me. I hadn't run D&D, and only played a few times, during the 3e era. Back in the 90's I ran a very heavily plotted 2e game set in a specific region of my old D&D home brew setting (maps from days predating even the existence of D&D in some cases, lol). Anyway, when I started the 4e campaign I wanted to just let the players establish what they wanted to do, so I just extrapolated the happenings from the old campaign a few years forward in time, and described the PCs as being in the largest town in the midst of a large crowd of refugees who appeared to be packing up into organized groups and heading out for somewhere.
The players established their own backgrounds, and I just answered a few questions they had from my existing material, or told them to go ahead and make stuff up. IIRC there was a Warlock from a far southern continent, looking for his father. There was a dwarf fighter trying to find some of his family members who were apparently refugees. There was an eldar (eladrin, but I gave them a bit different flavor) wizard girl running away to the world. There was a young woman who's family held a fiefdom on the borders to the south and sold their services as spies, who was supposed to be gathering info. There was also a priestess of the Sun God, Lir, who supposedly had a prophesy told about her birth (never 100% established what it meant of course).
The players didn't really firmly establish exactly why they established themselves as a group, but the gist of it seemed that they were all recruited by a local land holder to escort a bunch of refugees back to a village from which they had fled during the war (in the previous campaign). So the PCs were given directions and a factotem to accompany them and insure that they performed their escort duties. IIRC a few subplots quickly developed. The factotem (and his boss as it turned out) was an unsavory sort, and some of the PCs made an enemy of him right off. It was also established that the dwarf came on this specific trip because he had learned that his relatives had worked in the village the PCs were headed to.
Along the way I presented them with choices of which route to take. They decided on a bit less safe, but shorter, option, maybe at the urging of the factotem who was only concerned with being in a hurry. As a result they met up with some goblins and got to test out the combat system. They then tracked down the goblins to an old estate nearby and I wrote up a very small 'dungeon' for them to take on. IIRC there was a hook here that pointed at some kind of 'boss' that the goblins might be working for.
The party then traveled through a town, where there was another adventure. I'm not sure I recall all the details, but there was a monster of some sort operating as the ruler of the town and pretending to be a human, along with some of his minions. They plotted to break up the PCs, but the characters managed to thwart the plot, after a few hijinks. In the process they made some allies in this town and established the basic structure of its politics and such, but it was a pretty small place and they moved on after a couple of days.
Finally they reached their destination, there was some sort of blow up with the local ruler, due to his questionable treatment of his people. At this point the party used strong arm tactics, threats to get the priesthood of Lir involved, etc. to extract some better behavior, but it was now established that there was a creepy manor full of villains down the road! However the PCs ignored this story line. Instead they decided to investigate the nearby Forest of Grin, a wild and dangerous area known to be full of monsters. There were 2 reasons, the dwarf learned that his relatives might have been taken into the forest, and more goblins from the tribe they had encountered before were spotted scouting the village. Although the lord refused to officially commission them, they all felt that they could help even if they didn't get paid much.
After this there were various forays into the forest. I don't recall all the details of each one, but they discovered that most of the goblins were peaceful, but one faction had put itself into the service of some sort of mysterious personage. There was some fighting with those goblins, a battle against a couple of Hill Giants (turned into lower level solo/elite monsters IIRC), etc. The spy character established that she was in contact with her people and was sending them intel about this area, the dwarf had his motive, the wizard's family tracked her to the village, and the warlock's patron gave him a sign that he was pleased with the dedications of monster souls (it was a starlock, the patron is some sort of creepy elder being from the 'far realm'). So the PCs finally just launched themselves deep into the forest and discovered that there was indeed some sort of evil big bad brewing. In the process they fought a bunch of fun fights. The one against a very Cthulhuoid demon called "the thousand legged one" being the most fun. All of this was pretty much a 'mini sandbox', the PCs just traveled around the forest as they wished. Finally they got to a point where they were outclassed by the monsters 'on the mountain', and decided they would go back to civilization and follow up on various clues about a 'Well of Stars'.
I don't recall without going back through all the player's notes exactly which things happened after that in what order. There was a series of adventures in an ancient dwarven city, and the PCs took over a small fort (this was in an area a ways from the original village). Eventually they figured out part of the Well of Stars, which related somehow to the warlock. There was a story arc in which the PCs went to a neighboring kingdom to chase after a Palladin they rescued from the dwarf city whom the eladrin wizard had a crush on, but then he ran off to fight some war and they broke up. There was also a scenario with a white dragon in an ice cave, and the establishment that there was a nation of warlike hobgoblins on the other side of a mountain range, etc. etc. etc.
At some point the PCs went back to the original village and ran into a nasty hag who almost managed to eat two of them. A warden (I think it was a Goliath, we were into PHB2 by then). Around this time the PCs were into paragon tier. So at that point I started to make things more fantastical. They went to a flying castle/mountain and expelled an invasion of demons, and then got on the track of an ancient vampire who was one of the kingdom's powerful nobles. That eventually lead to the PCs entering the Shadowfell (somewhere in there they also went to the Feywild and the warlock acquired a second patron, a hag, and they tussled with a copper dragon and some Fomorians). During the flying castle they also established a quest to find the artifacts related to the first King of Kinergh, and some mythology establishing that he was supposed to 'return' at some point, etc.
All of this stuff drew both on extrapolation and use of existing material that I had left from decades of previous campaigns, but also simply asking the players what was going on, who they were, what did you find, etc. I think the eladrin wizard PC was retired at some point, she had one big arc with the paladin and then seemed kind of played out. A Warden was added, but that player left after a while and the character fell out of use. The dwarf ran into his uncle at one point, a former PC from a 1970's era game! Their were a LOT of details, much of which I can't remember precisely 10 years later, but the material was pretty dense and a huge amount of stuff got added. There was a whole set of themes. It was established that behind the scenes there is an ancient ongoing battle between chromatic and metallic dragons which shapes a lot of history. There is some sort of cosmic danger to the world that relates to this 'Well of Stars', there is a big evil bad guy up in the mountains. The ancient dwarf city is actually a fortress established to plug up the Drow's route to the surface (and the PCs accidentally damaged the seal). The kingdom to the east is now caught up in a civil war where one side is pacted with an arch devil. To the northeast a subarctic hobgoblin kingdom has found the 'Invincible War Banner' and they are now making war on their neighbors. Lots of stuff happened. We never really progressed beyond the vampire lord scenario for some reason, and this game has been 'sleeping' for several years at mid paragon. I'm not entirely sure why, it was an online game to start with (using Maptool) and it wouldn't be hard to continue.
Basically things started out pretty much along the lines of "run around in this setting, which is effectively a sandbox because there is so much old stuff lying around" but by the later parts it was getting pretty unscripted. I think I did create some maps and whatnot to use for the Shadowfell part of the Vampire thing. In the campaigns I ran after this (all set in a different area of the same world) I did nothing more than establish the existence of some towns, their basic features, and some NPCs were developed and then fleshed out as-needed. I also borrowed some thematics, like the dragon conflict is also active in that area, so interactions with dragons sometimes happen and that might come up as a ready explanation of whatever plot element is needed. This kind of thing can be useful, and since some of the players have been common between several of those campaigns it does create some sense of consistency. OTOH this kind of metaplot IS restrictive, and we have discussed some completely different premises that would require a whole new setting, presumably with a lot less 'myth' attached.