Naruto wasn't able to complete the Genin exam for some time. Either he was just a young starter and Sakura & Sasuke started after he failed, or a result that he was quite older. They say he was the same age, but never really told us to which day he started.
Doesn't that mean Naruto is older than Sasuke and Sakura?
As per this question and the Naruto wikia, Naruto was 12 at the start of the show. The Naruto wikia also lists Sasuke and Sakura as being 12 at the start, which indicates that they're the same age. It's also corroborated by this, which says it got it from the Official Character Stats Book.
As you point out, it's not really clear how that works out, given that he's stated to have failed the exam to become a genin more than once (I'm assuming that's what you're asking about, rather than the Chunin exam, given context). Possibilities for that include either that he started younger or that it's just a timeline mess that they never bothered to deal with. I'm guessing the latter.
It says that he failed twice + the last time where he ended up passing after all when he learned the Kage Bunshin. I read somewhere that we are shown he starts at the same time as the other contemporary genin, and we know he was in the same class as Shikamaru, Choji and Kiba, as they skip class several times, and Sasuke as they start their rivalry early.
I would guess that there are Genin-exams three or four times a year or maybe 3-4 times over a few months, and maybe extraoridinary tests for exemplary students that want to take it (itachi, 4th hokage, kakashi). Then they start their time as Genin at the same time no matter what, so everyone can be assigned to a proper genin-team with the best balance according to strengths and weaknesses. Sasuke being overall exemplary, Sakura super-smart but not very athletic and Naruto being quite athletic but not very school-smart makes for a very balanced team.
As some mentioned, it might change according to peace-time and war-time, or maybe in accordance to how many students there are. When looking at Boruto-classes (yes I read that as well. I have a lot of time.) there one is a repeater as well. 7times I think? and he is clearly older than the others, but probably not more than a year or so since he still seems on the same wavelength as the other kids.
Naruto is actually younger than Sasuke and Sakura, but it is stated more than once that the rookie 9 were all born in the same year. Shino is the oldest (born January 23). Sakura is the oldest of team 7 (born March 28).
In Shippuuden, Kushina, Naruto's mom, talks to Sasuke's mom, who is holding baby Sasuke, in the street just days before Naruto's birth.
According to the manga canon, Sasuke's birthday is July 23rd and Naruto's birthday is October 10th.
In Naruto, the standard Academy curriculum is 4 years of classes, and students usually enrol around age 7 or 8 and graduate around age 12. It is not mentioned whether there is some sort of civilian schooling prior to that age.
Genin hopefuls in Naruto could originally enter the Academy as soon as their parents deemed them ready, with some entrants (usually from ninja clans) being as young as 4 or 5, and could choose to take the graduation exam as soon as they had been enrolled a year (like Kakashi, who graduated at age 5).
Since it is not clearly shown/stated it is possible that Naruto enrolled early or that he just took the exams early by his own choice or being pushed by teachers who wanted to get rid of him, as it is also stated in the opening arc that if a student fails the graduation exam 3 times he cannot become a genin.
If you remember, Kakashi finished in a year, so I would guess that you could take the exams at least twice a year and Naruto failed 6 times. It never said how long they were at the academy. So it would make sense that they could be the same age.
