Forests are not perpetual carbon sinks, as trees eventually die and then decompose, releasing their carbon back into the atmosphere.
At best, a young and growing forest can be a temporary carbon sink, until it reaches maturity (and steady state).
Alternatively, a forest might support continual carbon sinking if and only if the recently dead and/or mature trees were somehow harvested and treated/stored in such a way that their carbon would not decompose and re-enter the rest of the biosphere.