There is no single definition. Allocator emerging-manager programmes usually set thresholds on AUM, years since launch and fund number. Many emerging managers ran money before launching, as proprietary traders, portfolio managers at larger firms or through managed accounts and on-chain vaults, but lack the fund vehicle and institutional operations allocators require.
The main obstacles are cost and time: a standalone fund launch runs to six figures and months, and the fixed cost of service providers makes small funds uneconomic.