Starting a campaign is hard. Not so much because it would be difficult to come up with a good main story or where it will all be heading to, but because it really isn't easy to come up with things for 1st level PCs to do, which they can handle and won't be over in under 1 hour.
If we regard 1st level characters as professionals who have completed their training and have enough experience in their field to head out on their own without a master or superior being in charge, what would be appropriate tasks for them to deal with?
I have come to believe in being epic in the story hook. The first session should establish the overall theme of the campaign, even if the PC's themselves are not able yet to influence the events going on around them to a large degree.
My general approach to this is to make the PC's initial role to be observer/survivors/small scale participants of larger events moving around them.
For example:
1) An overwhelming invasion - the Battlestar Galactica/Dragonlance/Zombie/Independence Day scenario. The PC's are initially in the role of refugees, or shepherds/protectors of weaker refugees as all heck breaks out around them.
2) An attack by an overwhelmingly epic monster - the Godzilla/Attack on Titan scenario. For example, the PC's are in a large city which is attacked without warning by a great wyrm dragon. The PC's are of no more interest to the monster than ants under foot are to a warrior. The PC's watch from a distance as the great heroes of the city are slaughtered, and must flee and survive the side effects of this dramatic event while providing what aid they can - a firestorm in the city, collapsing buildings, panicked mobs, runaway wagons, thugs taking advantage of people's terror/acting on their own fear.
3) An massive 'natural' disaster - the disaster movie scenario. The PC's are ordinary people that must come to grips with a tsunami, earthquake, hurricane, partial extinguishing of the sun, asteroid impact, magical plague, shattering of the world into floating fragments, etc.
4) A political coup occurs - the Hamlet/Game of Thrones scenario. A politically traumatic event has occurred, and the PC's are positioned so that they are aware that the public version of events is a lie, and a pretender has usurped the throne. The PC's must act to keep the fact that they know secret, or else flee as 'traitors' if they cannot.
The reason I've learned to do it this way, is if you start the campaign with a couple of sessions of, "Doing things that I know 1st level characters can do.", the players aren't necessarily aware that there is anything 'cool' for them in the future. Starting the campaign with a 'bang' is justified for the same reason that placing a big hook in the first page of your novel is justified. You want to ensure that the readers keep reading instead of dismissing the whole story as trite. If in the second session, the players are 'killing rats in a basement', in the context of the first session they'll know this action has larger meaning and importance beyond just being a leveling treadmill. Those small survival related tasks are part of the larger 'cool'.
From there, you progress the campaign with the players first learning more about the events that led up to the first session and the enemies that they have that are behind the mess, to gradually taking on the role of being the ones with the power to rectify the situation. This can lead you in a complete circle, where the PC's are tasked with handling what had been impossible before - facing that previously unfathomably imposing great wyrm from scene 1 of the story.
My current campaign began with a massive tsunami that the players had to figure out how to survive (running up hill as fast as possible being the easiest and most obvious option). Assuming that the players survived this, they then needed to decide what aid that they wanted to render to the survivors (or for example, to become looters). In the wreckage of the city were also a number of monsters washed up from the deep, as well as washed out of basements and other dark places they'd previously took shelter. There were also a number of newly created minor undead/haunts. The initial scenario was designed to be sort of 'sand box' style as players encountered looters, traumatically injured persons, people trapped beneath rubble, dead bodies, the occasional monster, important NPC survivors, and so forth.
