The first pre-Númenórean Men crossed the Great River into western Middle-earth in the early centuries of the Years of the Sun. The Númenóreans started to return to Middle-earth in II 600, but at first their influence was limited. It was only later that they began to found true settlements (notably Pelargir in II 2350), and only after the Downfall of Númenor in II 3319 that they began to rule over their own kingdoms.
The transition from pre-Númenórean times to the rule of the Dúnedain, then, can be seen as a gradual one, extending over a period of about a thousand years. There were indeed still Men of the Mountains dwelling in Ered Nimrais when Gondor was founded, but we can take the establishment of the South-kingdom as the final definite end of the pre-Númenórean period.
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