Membership in a good community is itself a form of social capital that you can even put an monetary valuation on (compared to not having a good community). Many immigrants arrive with that form of capital intact, and admission to such communities is often gated by cultural barriers.

Further, educated immigrants, while they don't start in their adoptive country with much money, arrive with a lot of educational capital, which someone invested in before they arrived. They arrive with the "tools and opportunity" built in.

For less educated immigrants, and native-born poor, assuming a functional community exists (which is not a given for either), it's members might be able to scrape together proceeds gained by expending their physical capital in marginal labor, and share resources among themselves (housing, childcare, etc.).

But depending on their circumstances, that may not be enough to move their members out of poverty, as the surplus of their labor may not be enough to pay for, in your words, the "tools and opportunity" needed to escape poverty.

Sometimes the requirements for the community's survival can actually hinder the acquisition of tools for advancement, i.e. a 16 year old has to take a menial job to help support the extended family instead of staying in school.