It's known that ancient Egyptians had a number of animals that were kept as pets, which include dogs, cats, monkeys, birds, and even gazelles. Mummified animals are often found in the tombs of the ancient Egyptians. Food for the pet was also included in their tombs. Dogs are thought to have been the first animal domesticated by the Egyptians. The Egyptians named their dogs just as if they were another family member. It's believed that cats were also first domesticated by the Egyptians and they rose to being adored and worshiped. The feral cats were vital to ancient Egyptian life because they killed rodents and snakes. They became domesticated and became companions to mostly women. Monkeys were kept, especially by the wealthy, mostly for entertainment purposes, and often were adorned with gold jewelry. Gazelles were often kept in the palaces as pets because of their gentle nature.

There are references to "tame" animals in the Bible. In Genesis 9:10-11, in the story about Noah and the flood, it says: "all the birds,and the various tame and wild animals....Never again shall all bodily creatures be destroyed by the waters of a flood"

And again, in Psalm 148: ""Praise the Lord from the heavens....Praise him, sun and moon; praise him, all you shining stars....Praise the Lord from the earth, you sea monsters and all depths;Fire and hail, snow and mist, storm winds that fulfill his word; You mountains and all you hills, you fruit trees and all you cedars; You wild beasts and all tame animals....Let the kings of the earth and all peoples....Young men too, and maidens, old men and boys,
Praise the name of the Lord..." (v. 1-13).

It seems apparent that God intended for some animals to be pets and companions for people and pets have been a part of human living since the beginning.

Humans started taking animals as pets on a widespread scale shortly after the discovery of beer. This was in the Mesopotamian region between 10000 and 15000 years ago. The phenomena are interrelated. When humanity discovered beer it needed a stable supply of grain, originally emmer and barley. This led to the adoption of an agricultural lifestyle, which replaced that of the hunter-gatherer and in turn led to settlements and civilization. Wolf-like companion animals became domesticated and evolved in form to dogs to suit the changed human diet and its leftovers. Cats were attracted to feed on the rodents that were in turn attracted to stored grains, and were welcomed by humans and made pets.

While that was the origin of the widespread adoption of pets, there can be little doubt that the process also plays off the maternal instincts which are older than humanity itself. On an occasional basis even stone age level tribesmen in the tropics adopt young wild animals as pets. Even other species are known to do so. It seems to be a side effect of the maternal instinct of all mammals. It may even be related to the parental instincts of birds that allows the European cuckoos and the American cowbirds to take advantage of other species.

Ever since humans were created (which no one would know the actual date of), man has enjoyed company from something that shows love and affection without answering back or disagreeing with your thoughts

It is not sure when did human started keeping animals as companion or pets.

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Historians are not sure when humans first started keeping animals as pets. Keeping an animal for pleasure rather than for food or work was possible only for people who were well off and had the resources to feed extra mouths. Dogs most likely were the first pets, because they were domesticated so long ago. The ancient Romans are known to have kept pets, particularly dogs and birds. Cats and horses were also popular with Romans and may have been considered pets, but they were also working animals. The origins of ornamental goldfish date back to the seventh century in China, where Buddhist monks first raised them in ponds. By the fourteenth century the Chinese were keeping goldfish indoors in bowls as pets.

During the Middle Ages many pet cats were put to death with their owners on suspicion of witchcraft. It was during this period that dog breeding became popular in Europe. Although many dogs were bred for herding, guarding, and hunting traits, some breeds were tailored to pet owners who desired certain coat characteristics, sizes, and behaviors. Pet ownership was mostly limited to the upper classes of society—royalty, aristocrats, and landowners.

The first American colonists brought a few pets with them to the New World, but life was hard in the colonies, and resources were scarce. Few people had extra food to give to an animal unless it was being fattened up for slaughter or earning its keep by working. Some dogs and cats may have been called pets, but they also performed useful tasks such as guard duty and killing rats. The modern age of pet keeping began in the mid-1800s, when a thriving middle class emerged in society. This was the first time that many people had the time and money to keep animals solely for companionship and pleasure.

According to historian Kasey Grier of the University of South Carolina, tropical birds, such as parrots, were highly valued in American society before recorded music became available. They were the first animal companions for which goods were specifically marketed, including bird food, medicines, cages, and other accessories. The Pet Food Institute reports that the first commercially prepared dog food was introduced in England around 1860. The first goldfish were bred in the United States in 1878. Canned dog food was introduced in the United States following World War I (1914–18). Dogs, tropical birds, and ornamental fish were the house pets of choice well into the twentieth century. The keeping of horses for personal enjoyment rather than for work also grew. In 1947 cat litter was introduced to U.S. consumers, making it much easier to keep cats indoors. They too became prized as pets and eventually surpassed dogs in popularity.
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I cannot tell for sure but I remember having seen pets like dogs or cats appearing in famous paintings, hundreds of years old which means that people started having pets a long time ago.