In terms of food and security, I would argue that the Jamestown/Virginia colony became self-sufficient sometime during the Second Anglo-Powhatan War of 1622-1632. Prior to this conflict the colony frequently had to be supplied with infusions of food either from English supply ships or from exchanges with the Powhatan people. Furthermore, the Powhatan people had the military potential to prevent the English colonizers from farming and sustaining themselves as they did in 1622, causing mass starvation in Jamestown.

The 1623-24 campaign broke the power of the Powhatan people to oppose the English. Through a poisoned meeting and a strategy of pillage and arson, the English pushed the Powhatan settlements far enough away that Powhatan raids could not threaten the farmland occupied by English settlers. Nor did the English stop after merely gaining the upper hand, they pursued a relentless genocidal campaign of "fieringe and wastinge" against the Powhatans and their food supply for the next 8 years.

At some point during this campaign, it was clear that the English could not starve or be starved out.

Self-sufficiency in tools is difficult to address. The colonies were always a net importer of finished goods and tools, because the western frontier was simply a profitable place to deploy saws, axe heads, plow shears, knives, guns, others weapons etc. Essentially the colonies could turn these items into valuable land or cash crops to export back to Europe. So the flow of tools into the colonies always persisted in the same way the flow of people (both free and enslaved) did. Regardless of immigration, it was clear that the increase in population was a trend that would continue after the Second Powhatan War.

Sources: Horn, James 1619, Jamestown and the Forging of American Democracy

Rice, J. D. Second Anglo-Powhatan War (1622–1632). (2015, November 30). In Encyclopedia Virginia. Retrieved from http://www.EncyclopediaVirginia.org/Anglo-Powhatan_War_Second_1622-1632.