The short answer: Europeans didn't dominate the local population quickly. Or at least, not always.

The long answer will focus only on British North America in the 1600s and 1700s. There was a lot of variation from place to place, and the situations with the Spanish and the French are quite different.

The way the question is phrased reflects a common way that modern Americans think about early American history. That is to say, people might know a little about early colonization (say, the Pilgrims and Squanto, or Pocahontas and John Smith). They might have a vague sense of later colonial America -- maybe some idea of sailing ships or women in long dresses or Ben Franklin working at his printing press, or something. And then they might leap straight to the American Revolution. As a result, the colonial period appears very short, and Indians mostly appear only at the beginning.

But this is not accurate. Jamestown, Virginia, settled in 1607, was the first permanent British colony in North America. The Revolution broke out in 1775. During this period of 168 years (and later, for that matter) colonists engaged with Indians all the time, and not always from a position of strength.

Looking only at the colonial Northeast:

The Pilgrims arrived in 1620. A larger group of Puritans arrived in 1630. In 1637, a significant Indian war known at the Pequot War took place. In the Pequot War, the English colonists exploited pre-existing Native American rivalries, making an alliance with the Narragansett Indians and nearly wiping out the Pequots.

But the Pequots were only one nation. Other Native Americans continued to live near the English, and tensions between the colonists and the Indians increased in the following decades.

A much larger war (King Philip's War, or Metacom's War) took place in 1675-1676. King Philip (also known as Metacom or Metacomet) was a Wampanoag leader who successfully united members of various surviving New England groups, including the Wampanoags, Nipmucs, and Narragansetts, to resist continuing English expansion. He united about 2/3 of the Indians in Massachusetts against the English, and the war was catastrophic for both sides.

By this point, there were ninety English towns in Massachusetts, and the Indians attacked fifty-two of them. About 2500 colonists died in the war -- roughly five percent of the white population of Massachusetts. But the Indians lost, and the war probably (directly or indirectly) reduced the Indian population of the region by about 40%. This number includes Indians who died in battle (including Philip himself), starved to death when their fields were burned, fled the region when the war was over, or were sold into slavery by the victorious colonists.

But this is hardly the end of the story. The Pequots had been demolished, and King Philip's alliance had been shattered. But if we move forward in time, we find the English in Massachusetts, New Hampshire, and Maine still living in fear of the Indians.

Remember: the French claimed Canada for much of the colonial period. The French were rivals to the British and made alliances with various Native American peoples.

When England and France fought in Europe, their wars spilled over into America. In 1688-1689, the colonists faced the French and the Indians in King William's War. In 1712-1713, another war (Queen Anne's War) broke out. Colonists in these wars fought in battle against the Indians, and colonists were also captured in Indian raids. We are now almost 100 years since the Pilgrims arrived, and Indians are still resisting colonization.

Indians also fought in the Seven Years' War (1756-1763) and the American Revolution. In the Revolution, most sided with the British, recognizing that the expansionist Americans were a greater threat to their way of life. After the Revolution, when the Indians learned that their interests had been entirely ignored in treaty-making, and that the British had given their lands to the Americans, war continued.

Now, I've been focusing only on warfare. And you may have noticed that the general pattern is indeed one of loss. The Indians lost in the Pequot War and King Philip's War, and later wars. Why?

There are multiple factors involved. One very major one (as another poster mentioned) is epidemic disease, which tore through Native American communities repeatedly, making it much harder for Indians to resist European expansion. Others include land loss, cultural dislocation, and losses associated with the fur trade.

On the other side, the white population of the British colonies was increasing very rapidly, due both to continued immigration and natural increase. As the colonial population (made up mostly of farmers) increased, colonists kept moving west in search of land. As they moved west, they came into contact with Indians who were suffering from disease and other effects of colonization. When warfare happened, the more numerous and healthier colonists usually won.

So, TL;DR: The English did come to dominate the Indians. But (despite the crushing effects of epidemic disease on Native American populations) they did not do so quickly or easily.

Selected readings:

Daniel K. Richter, Facing East from Indian Country: A Native History of Early America (2001)

Katherine Grandjean, "The Long Wake of the Pequot War" Early American Studies 9: 2 (Spring 2011) 379-411

Christine DeLucia, Memory Lands: King Philip's War and the Place of Violence in the Northeast (2018)