We don't know, and the aging of regular characters - especially Carl - is probably not the best way to guess, but we get a ballpark estimate by looking at Judith.
Carl has been played by Chandler Riggs throughout the series, so the producers had no way to slow down the actor's maturing. With Judith, however, the producers have been swapping out babies on a regular basis to make sure the character ages slowly. So far, 16 babies have played Judith.
In most of season one, all of season two, and part of season three, Judith had been conceived, but not born. She was conceived either by Shane and Lori while Rick was in his coma, or by Rick and Lori immediately after he found Lori and Carl.
By season six, the role had fallen to Chloe and Sophia Garcia-Frizzi. Judging by the photo below, the twins appear to be roughly 18 months old:
Since the producers have chosen actresses who are the right age for the part, we can use this to work out how long ago the inevitable zombie apocalypse began.
- Judith was born 18 months ago.
- She was conceived 2 years, 3 months ago.
- The inevitable zombie apocalypse was already underway when she was conceived, but had begun no less than two weeks earlier, when the world went to hell, and no more than a month earlier, just after Rick went into his coma.
Thus, the inevitable zombie apocalypse began roughly 2 years, 4 months before the events of the season 6 finale.
Basic timeline of season premieres and finales:
Rick wakes up no more than a month, and no less than two weeks, after the outbreak became unmanageable and the infrastructure began to fail; the season ends about a week later, when they leave the CDC.
They get stuck in traffic the day after they leave the CDC; the farm is overrun no more than a month or so later, ending the season.
The season begins with the group on the road, having spent the winter wandering from place to place, and Lori is visibly pregnant; the season ends a month or so later, when the Woodbury survivors join the prison group.
A few months have passed since the end of season 3 - the Woodbury refugees have become a part of the prison community, and a farm has appeared where there had been only an empty yard; the season ends a few weeks, perhaps as much as two months, later, when the group reunites at Terminus. Judith hasn't aged much in this time, and even in season 5, she doesn't look much older.
Judith, early in season 4 (left), and in season 5 (right)*
The escape from Terminus in the season premiere happens within hours of Rick's arrival there (Carol is drawn to the site by the sound of the gunfight between Rick's group and the Terminites, which concludes with Rick's group being captured); the season ends with Rick killing Pete a few days after they join the Alexandria community. It seems that all of this takes place over the course of a couple of weeks, probably less than a month.
Judith, early in season 5 (left), and late in season 5 (right)*
In the season premiere, not much time has passed since the season 5 finale - perhaps a few days. The first half of the season - from the attempt to herd the walkers in the quarry, through the Wolves' attack and walker invasion, and up to Carl's gunshot wound - takes place over the course of two or three days.
There is a two month time jump between episodes 8 (the midseason finale) and 9 (the midseason premiere) - Carl's eye is healing, the walls have been repaired, etc. The second half represents another week or so.
Judith, season 6 premiere (left), and second half of season 6 (right)*
In season one, episode five, Wildfire, Dr. Jenner says:
It's day 194 since Wildfire was declared and 63 days since the disease abruptly went global.
This episode takes place the same week Rick woke up, about a month after the inevitable zombie apocalypse began in earnest. Thus, the first zombie appeared at least six months before Rick woke up (about 5 months before he went into the coma), and isolated cases of zombies had spread around the world at least 2 months before Rick woke up (about a month before the coma began), but it wasn't common knowledge.
After all, Rick had clearly never heard anything about zombies before his coma, because he was totally bewildered when he finally saw one. As a sheriff's deputy, he is a first responder, and would presumably have heard about the crisis as soon as it became an issue in the US.
Thus, the first zombie appeared almost 3 years before the events of the season six finale, and zombies had been spotted around the world 2 1/2 years before the end of season 6, but the world didn't end for another 5 months after the first zombie popped up.