Statements of age requirements vary somewhat. Frequently cited is the 10-12 age range, for physical reasons. However, there are examples of people much older than that becoming Space Marines. Luther (kind of...) and Kor Phaeron are the only examples of full-grown adults becoming Marines, while Ragnar seemed to be in his late teens judging from Space Wolf.
I'd guess that 10-12 is optimal, for genetic modification (and also you have the benefit that they're still reasonably young and impressionable), but it can be pushed up to 18 or 19 and still done, albeit with more risk. Many Chapters like to wait until that age for reasons of tradition, so that the aspirant can achieve various trials first, such as fighting in combat, apprenticing to a blacksmith, killing a barbed dragon, and so forth.