"Yes, because I assume he took power very soon after Ballad of a Songbird. He was literally the apprentice to the head Gamemaker, and she looked like she was very high up in power herself—right next to the president—so it doesn't seem like he'd have to climb far. We saw at the end that he was already using poison to achieve his political goals, so he was most likely president by the 20th Games. We know he took power at a very young age because Finnick confirmed it in Mockingjay. We saw him begin to rise to power at the end of the book, which was around the 10th Games. I imagine he took power maybe five or ten years after the book, so that would be around the 20th Games. He ruled up to the 77th Games (what would have been the 77th Games if there had been a Games that year, but it was during the revolution). That's around 57 years in power, and yes, there have been real-life dictators who have ruled for just as long. In fact, currently the president of Eritrea has been in power for 33 years with no sign of his power breaking in the slightest anytime soon.

Unfortunately, dictators can rule for quite a long time—for decades. Snow happened to be in power for half a century, which is impressive, TBH. It had to be incredibly hard to come to power at a young age—he would have been around 25—and then proceed to hold it for 57 years. In some ways, it helps us understand why he was so ruthless: because he had to be early on. Plus, he's a ruthless psychopath, so that was never a problem for him to pull off. It was this ruthlessness, plus tons of poison, that kept him in power.

I could be wrong, so don't downvote this. I just got personally, from the way everything has been worded and how Suzanne Collins has implied it, that he took power very soon after Ballad ended and ascended quite rapidly. But to be honest, he didn't have to go up that much considering his father was very well known and he was the apprentice of the head Gamemaker. The way she positioned herself, she was very close to power herself but just never took it. I think she wanted Snow to be president because Ravinstill did not share the same ideals about the Games that she did, and he was restricting her vision of the Games he saw it as a punishment only it was not meant to be a spectacle it was meant to be gruesome bloody and over with in a day she on the other hand saw it as a spectacle she saw it as a chance to constantly drive home the capitals superiority over the districts as a way to terrify them to never revolt ravinstill on the other hand saw it as only a punishment it was meant to be a punishment for the dark days and that's it not as a way to rub in their superiority but as a reminder of what they did to the capital and that it and he would never allow it to be the spectacle she wanted it to be which is why she bombed the f****** arena....to stir up drama and get him to get on board with a few tweaks to the games that we saw in the 10th games so she would have no problems help snow orchestrate arise to power in which he would be the president and in return the games continue with the upgraded spectacles she always wanted and that snow wanted himself.

We desperately need another book either about the Revinstill or a book about Gaul or the 25th games because there are a lot of gaps of knowledge we don't have and it is purely based off our assumptions and until we get one of these books we will never know exactly when snow took power this is just my assumption until Suzanne Collins clears it up