People will give you varying times--anywhere from a few weeks to a year--so I try to make it easier by saying that as long as you have a healthy growth for coralline algae, your tank should be suitable for an anemone. It could take weeks or months for coralline to really take off, but it's a good visual indicator, and there really isn't any guessing--it's either thriving or it's not.
The reason I say this is because all tanks mature at different rates, but the requirement for coralline to grow is always the same: good lighting and water parameters are stable with alk/calcium at consistent levels.
These are the same requirements needed for anemones.