Where would the animal be transported from to get to the zoo? If it's the wild, that could pose some problems. For the most part, you can't catch a mammal in the wild and transport it to a zoo-- most exceptions include animals that are rescued (like an orphaned baby bear or an animal injured in a wildfire) or an animal illegally smuggled into a country that's confiscated at customs and sent to a zoo.
More typically, animals are transferred from one institution to another. If that's the case, you'd have to figure out why this zoo qualified to be the one American zoo displaying this species. If the animals are on a breeding loan (like pandas), you'd typically acquire two of them in hopes of propagating the speccies.
Some animals that don't exist in US zoos but exist in other countries' zoos are proboscis monkeys, Javan rhinos, and golden snub-nosed monkeys.
Some animals that don't exist in zoos at all are also not in zoos because they're really hard to keep alive. For instance, mountain gorillas and great white sharks and and the single rarest animal on earth, the vaquita, have so far not survived in captivity. Proboscis monkeys in the US did fall into this category, so if it's an animal like that, your protagonist would have to have some compelling new method for caring for this creature that previous US zoos haven't used.
EDITED: Moved vaquita to the correct paragraph
Another possibility would be if the animal was something thought to be extinct, like a thylacine or a quagga, that was illegally imported into the country by a private breeder.
