While my knowledge of colonialism in Brazil and Argentina is limited, I can discuss the factors influencing colonial population growth in the Eastern U.S. between 1630 and 1700. To do so I'll be borrowing bits from earlier answers I've written for this, and other, subs. The answer to your question stems mostly from slowly building on established English colonial footholds, and then breaking out from those footholds through the constant assault on Indian bodies and lands.

The first few centuries following contact were met with disastrous European (really mostly Spanish) forays into North America. While they managed to tenaciously hold onto Florida, and needed to reconquer New Mexico, the Spanish persisted in tenuous outposts on the northern edge of a vast Empire. The southwestern colonies protected lucrative mining enterprises in Northern Mexico, and Florida provided a safe haven/support for ships crossing the Atlantic. For this protection, New Mexico lost the Crown 2,390,000 pesos in the 17th century alone. Florida cost four times as much. Though covering a wide geographic range, the total number of missionaries remained small; never more than 70 at a time for Florida, and < 50 for New Mexico. Numbers of other colonists, farmers, and soldiers were likewise small compared to the surrounding Native American populations.

On the Atlantic coast most early interactions with French, English, Dutch, etc. colonists were short-lived trading forays by visiting fishermen or slavers. Few long-term settlements survived prior to the start of the seventeenth century. After a century of small-scale European trade and exploration along the New England coast, Plymouth colonists arrived in Massachusetts in 1620 on the heels of a nasty epidemic. Population decline and pressure from inland enemies caused Massasoit, sachem of the Wampanoag, to change the traditional policy of opposing long-term European settlement. Instead of driving the colonists into the sea, he sought an alliance with Plymouth. The peace lasted a generation. When the dust settled on King Phillip’s War, the English colony barely survived. Over 3,000 Wampanoag, Nipmuck, Podunk, Narragansett, and Nashaway were dead. Native American survivors who were not confessing Christians were sold into slavery in the Caribbean. English colonists moved on to the newly emptied land and the colonial population jumped from several hundreds to ~55,000 by the end of the century.

In Virginia the story was much the same. Jamestown colonists arrived to Tsenacommacah (densely inhabited land) in 1607, a large area of tidewater Virginia under the control of the Powhatan mamanatocik (paramount chief) Wahunsunacawh. Wahunsunacawh/Powhatan responded to the encroachment of the Spanish from the south by allying more than twenty tributary groups under one confederacy, and through Captain John Smith established Jamestown as yet another tributary settlement within the greater Powhatan sphere. Again, the peace proved short-lived. The Anglo-Powhatan Wars and the aftermath of Bacon’s Rebellion prompted the establishment of the first Indian reservations, restricting the territorial limits for the original inhabitants of Tsenacommacah. Escaping the unhealthy swamps surrounding Jamestown saw a decrease in colonial mortality and the dependency on tobacco farming required not only land, but the souls to cultivate the crop.

As Virginia and Carolina grew an new manifestation of evil opened up land throughout the Southeast. Traders operating out of English Virginia and Carolina united the greater southeast in the sale of human captives and deerskins. The changes wrought in the English shatterzone, the displacement, warfare, disease, exportation of slaves, and famine, set the stage for the first smallpox pandemic from 1696-1700. The Yamasee War that followed threatened the survival of the colony of South Carolina, but the damage was done. Slaving raids collapsed the Spanish mission system, nearly depopulating the Florida peninsula. Survivors banded together, forming alliances of convenience, and coalesced into confederacies like the Creek, Choctaw, Cherokee, and Chickasaw. Slaving raids, warfare, and disease then left the southern tidewater open to English expansion.

Along the Eastern seaboard the toxic colonial cocktail of warfare, disease, territorial displacement, and slaving raids opened Indian land and allowed once-small colonial outposts to see near-constant growth in the later half of the seventeenth century. A century after initial contact more than two million people lived east of the Mississippi River. Less than five hundred were European. After more than three hundred years of war, epidemics, displacement, and maneuverings the descendants European colonists finally gained hegemony east of the Mississippi by 1820. The displacement of Native Americans from eastern North America was neither fast nor easy nor inevitable. That early population boom represents both the natural increase and arrival of migrants fighting to extend previous confines into a dynamic, changing New World.

I can't give a completely definitive answer, it's quite a complex subject and would require several thousand words to thoroughly explain, but a few points:

The various colonies didn't develop along the same lines - differences based on native populations, climate, farming conditions set the pattern for the way the colonies grew.

Spain conquered pre-existing empires (Aztec and Inca being the two major ones) and built their colonies around exploiting resources from the native populations, particularly silver and gold.

The Portuguese settled Brazil and created a plantation economy built on African slaves. Wherever a cash crop like sugar or tobacco could be grown the focus of the colony would become a plantation economy with the goods shipped back to Europe.

With the Spanish and Portuguese monopoly of Central and Southern America the English and French were forced to look to North America. The native populations of what is now the eastern US had been decimated by epidemics which were spread either through Spanish expeditions from the south or through early trading contacts with the English, Dutch and French.

When the first settlers arrived in New England they found prime farmland that was almost completely depopulated.

One colonist remarked, "Thousands of men have lived there, which died in a great plague not long since: and pity it was and is to see so many goodly fields, and so well seated, without men to dress and manure the same." Imagine how much more difficult the colonists' lot would have been if instead they had come to a crowded land of well-defended villages, or to a truly virgin continent without any already cleared lands.

Taylor, Alan. American Colonies (2003)

Another aspect was the English model of colonization, which differed from the Spanish and Portuguese models,

The English were in the lead and remained so. They prospered for two reasons. One was the technique, of which they were the first and most succesful exponents, of transporting whole communities, men, women and children. These set up agricultural colonies which worked the land with their own labour and soon became independent of the mother country for their livelihood.

Roberts, Westad. The Penguin History of the World (2013)

This allowed exponential growth when combined with a constant supply of immigrants. The population of Europe was rapidly growing due to the Columbian exchange which allowed many previous infertile or impractical areas to be farmed. The population of Ireland for example grew massively due to the introduction of the potato, but was then vulnerable when faced with a widespread blight of the crop (this was often seen in pre-Columbian native American populations where populations would collapse due successive crop failures).

There were also things like religious and personal freedoms which further attracted immigrants and the potential to escape from a rigidly hierarchical Old World (which had also been transferred to the new world possessions of Spain, Portugal and France). This was a significant attraction to other European emmigrants, "and after 1688 Scottish, Irish, German, Huguenot and Swiss emigrants had begun to arrive in appreciable numbers" (Roberts, Westad).

Also the almost symbiotic relationship between the New England colonies and the English West Indies. The Caribbean colonies allowed the stimulus and output for developing industries such as shipping, distilling and shipbuilding where New England came to compete with the mothercountry due to its vast timber resources. All these further promoted economic growth and therefore population increase.

The older Iberian colonies didn't grow as much because of their focus on plantation economies and exploitation of the natives. Mexico was built around the former Aztec empire and it's various native peoples, Brazil was a plantation economy of primarily African slaves and Argentina was never more than an afterthought to the Spanish administrations, the heart of the Spanish colonial empire being the gold shipments from Lima and Mexico.

I've paraphrased and simplified here. Any follow up questions I will try to answer but I highly recommend the book "American Colonies" by Alan Taylor for an extensive and thorough explanation of this question and almost any other around the colonization of the Americas.