How did apartheid start?

Although racial segregation existed much earlier, the formal policy known as apartheid began in South Africa in 1948 when the Afrikaner Nationalist Party came into power. The word "apartheid" comes from a word in the Afrikaans language meaning "apartness" or "separateness." The policy called for a systematic separation of racial groups throughout the country. The difference between apartheid and previous policies of discrimination was that apartheid made discrimination part of the official rule of law.
Under apartheid, the entire population had to be registered as members of the particular racial groups of white, black, colored, Indian, or Asian. The various racial groups had to live in different locations, especially in urban areas, and those who did not move voluntarily were forced to move. Over 80 percent of the land was set aside for whites, and non-whites had to carry documents that authorized them to move around in white areas. Rural blacks were forcibly removed from their land, which was then sold cheaply to white people. By 1950, it was against the law for whites to marry non-whites and for whites to have sexual relations with black people. Only whites could participate in national government, and non-whites had to use separate public facilities from whites.
The policy of apartheid met with protests and, in some cases, violent resistance. It also was condemned internationally. In 1976, the UN Security Council forbade sales of arms to South Africa, and in 1985, the United States and the United Kingdom imposed economic sanctions on the country. It was not until 1994, however, that a new national constitution was approved and apartheid officially came to an end.
https://www.history.com/topics/africa/apartheid

https://www.sahistory.org.za/article/history-apartheid-south-africa

Official apartheid policies in South Africa began in 1948 with the passage of a series of laws. De facto segregation, though, began with invasion by the Dutch Empire in 1652 and the resultant servitude and enslavement of Africans, Malays, and others. Very early on, the Dutch set up a racist hierarchy in which Europeans were at the top, mixed or colored peoples were in the middle, and Africans or "Bantus" (an offensive epithet) were at the bottom.
Many Dutch colonists moved away from the empire's control and killed and controlled large numbers of Africans; this led to a sense of racial entitlement. When South Africa became independent, Africans were barred from the government and most churches. A series of laws, passed by the National Party in the 1950s, banned mixed marriages, interracial sex, and nonwhites living in white areas, and classified everyone based on ancestry, appearance, and culture. Over three million Africans were forcibly evicted, and some lost citizenship.

The official beginning of Apartheid can be traced to the rise of the National Party in South Africa in 1948. However, this system did not simply occur overnight. It is important to understand the cultural and societal aspects of South Africa to gain a basic understanding of how and when Apartheid began.
Apartheid, or "apartness," started primarily with the systematic discrimination against black people in South Africa during the early 1900s. White South Africans saw black people as problematic, as they moved into the cities in large numbers. This racial aspect of South African culture, accompanied by the economic disasters of the Great Depression, allowed the white minority to transition into legislative action against the non-white majority.
Once the National Party gained control in 1948, one can argue Apartheid officially began. Multiple government decrees, such as the Population Registration Act of 1950 and the Separate Amenities Act of 1953, serve as glaring examples of the systematic racism entailed by Apartheid. The Population Registration Act essentially classified South Africans into four racial categories, and the Separate Amenities Act became the justification for the legal segregation of public places in South Africa.

If one were to have asked the late former President Nelson Mandela this question, he would almost certainly have answered that Apartheid began in 1910, when South Africa became a unified country with the passing of the South Africa Act. Racist policies in South Africa can certainly be traced back as far as 1913, with the Land Act.
Officially, however, Apartheid started in 1948, when the National Party came to power in South Africa. The National Party, made up exclusively of white people, immediately began to write the patterns of racial segregation that already existed in South African society into law. They wasted no time in doing this, and by 1950, the Population Registration Act dictated that every South African citizen be classified by their race, with black people being referred to officially as "bantus"—a term that is considered very offensive today.
https://www.history.com/topics/africa/apartheid