Warning: spoilers abound
Tl:dr: Start at the 4th module with Leosin and Ontharr giving the characters the mission.
You could start at the 4th module! The game expects the characters to be level 4 at this point, so there wouldn't be any balance issues. The only problem should be that your characters won't have the background from the previous modules.
However, the 4th module starts with the characters being given a mission by ranking members of the Order of the Gauntlet and the Harpers. So the simplest way to do this would be if your players' characters were members of the Order of the Gauntlet or the Harpers, in which case it's perfectly natural for them to be given this mission.
The only question remaining is how to supply them with the background provided in the previous 3 modules. Luckily, there's nothing there that isn't easily supplied as part of the mission briefing from Leosin Erlanthar and Ontharr Frume.
The first module can be easily summarised as "The town of Greenest was attacked by the Cult of the Dragon." In your campaign, it might even have been destroyed, since the characters weren't there to save it.
In the second mission, the characters rescued Leosin and discovered some valuable information. However, Leosin knew most of what they found out anyway, so you can simply say that he escaped on his own, and there won't be any gaps to fill.
In the 3rd module, the characters fought their way through a dragon hatchery and secured some eggs. They also killed a minor cult leader and discovered some bits of information, but nothing that really matters. The dragon eggs and the minor cult leader have no impact on the story (update: they have a slight effect in Rise of Tiamat, but it shouldn't be a problem for you), so you don't even need to mention them. The main bit of information was that "the treasure is headed north to Naerytar", which the characters wouldn't have understood anyway. So there's really nothing from the 3rd module that you need to include.
To sum up, simply start the characters at the start of the 4th module. Have Leosin and Ontharr tell them that the town of Greenest was attacked, and they want the characters to track a load of treasure that is heading north. Have Leosin tell them that he infiltrated the cult camp, and give them as much of the info from the 2nd module as you choose. (Or don't if you don't want to, there's nothing there that they won't find out later anyway.)