We aren't, there are other species with self awareness, bottlenose dolphins are a good example.

Crows and ravens are another.

It's even been theorized that certain animals, like whales, may have a higher aptitude for certain attributes we consider to be human, like emotion and empathy. This is because although human brains are large and dense, certain regions of our brain aren't as developed or active as whats has been observed in some animals.

Why would you assume that is a statement of fact?

Elephants certainly are

Chiming in to add elephants, African gray parrots, apes, orcas, and dogs (if using the sniff test rather than mirror test)

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Pretty much any creature with a brain is likely sentient to some degree. Also many animals are likely just as sentient as us, they're just not as advanced because they lack the communication abilities we have that allowed us to advance.

You know how you have a brain that helps you think and feel things? Well, different animals also have brains, but they are not the same as yours. Some animals have very tiny brains that only help them do easy things, like eating or sleeping. These animals may not think or feel much at all, or only a little bit. Other animals have bigger brains that help them do more things, like playing or talking. These animals may think and feel more than the tiny ones, but not as much as you. You have the biggest and best brain of all the animals, because it helps you do many wonderful things that no other animal can do, like reading stories, drawing pictures, singing songs, or counting numbers. You also have something very special that no other animal has: you can think about yourself and who you are. You can ask questions like “What is my name?” or “What is my favorite color?” or “How do I feel today?” This is called being self-aware or sentient. It means that you have a very special kind of thinking and feeling that makes you different from all the other animals.

There's also an open question of some cephalopods like octopi. We know they're very intelligent; but we're not sure how to test if they are self-aware.

I feel this question is going by a very antiquated assumption. Lots of animals are sentient. Dogs are sentient, cats are sentient, cows, pigs, chickens... and the list goes on and on.

We're not, there are many other species that are sentient. Certain birds exhibit the signs of sentience. Many mammals, including the great apes, pigs, dogs, whales, dolphins, and manatees can be self-aware. It has been suggested that even squid and octopi can be self-aware, although it manifests itself a bit differently than mammalian self-awareness. It is suspected that humans became better at language than other species (whales can rhyme and they give each other names, but don't have languages at human level), which allowed us to conceptualize at a much higher level and conceptualization lead to higher creativity, and our opposable thumbs allowed us to develop tools in a way other non-primates couldn't

Recent studies of sperm whale communication suggest it’s as complex as human language.

They even want to try using AI to talk with them: https://hakaimagazine.com/features/are-we-on-the-verge-of-chatting-with-whales/