The world of Westeros in Game of Thrones is not like the one fans know on Earth. Both planets are inhabited by human beings, but when it comes to flora and fauna, things are different. The most obvious are the dragons, the first of which have been born in over a hundred years. But they're not the only ones. There are direwolves, which are giant beasts, ten times the size of a regular wolf. There are ice spiders, kraken, white ravens, and shadowcats. But there are more normal animals too, like horses and elephants in Game Of Thrones, the latter of which Cersei was very disappointed to find hadn't come in her Golden Company All Inclusive Package.
While some fans were shocked to learn there are elephants, who are native to the lands of Essos, it's not like Westeros doesn't have its own equivalent. During Jon snow's time above the Wall with the wildlings, when he was infiltrating Mance Rayder's forces, he regularly saw mammoths in the wildling camps, which were ridden by the giants.
In fact, those mammoths were used in battle during the Season 4 episode "The Watchers on the Wall," when the Battle for Castle Black was fought. So it's not like they've been left out of the series.
Now, to be fair, mammoths are not elephants, though National Geographic says that the remains of the extinct Wooly Mammoth show them to be "more closely related to Asian elephants than to African elephants," and "the three species diverged within a surprisingly short period of time."
Elephants are more suited to warmer weather, and though Westeros has southern climates, it's not like Essos, which has large swathes of land known as "The Great Grass Sea" where elephants can live in large herds. According to the Game of Thrones wiki, the elephant is native to the Essos continent, as is their diminutive counterpart, the dwarf elephant. In the books, they turn up in the background as Astapor when Daenerys arrives, and she's gifted three of them when she conquers Meereen. Dwarf elephants practically overrun the streets in Volantis when Tyrion passes through the city.
The series, on the other hand, has mostly avoided putting expensive animals on screen as part of the background characters. For instance, the showrunner avoided using snowbears as part of the Castle Black siege or having them as part of the wildling encampment, even though the creatures are part of those scenes in the novels. In the end, they did find a way to work one in, during last season's "Beyond the Wall" episode.
Elephants are much the same issue. The show could rent them, or CGI them in. Alternatively, they could turn them into a running joke instead. Here Cersei spent all this money on The Golden Company and they couldn't even bring her one elephant across the Narrow Sea. The latter is a far cheaper option in a season that already busted budgets at every turn, and allows for Twitter to make Dumbo memes.
Just this once in Westeros, everybody wins.