Let's assess its feasibility first. In the point of the China military view, a significant portion of the Taiwan island occupation must be done before the US intervention. And their limited amphibious attack capability complicates the problem. Taiwan has 200k standing army and 250k more reserve forces, thus China probably needs to deploy at least 500k, preferably more than 1M of its army into Taiwan within a week or less. Otherwise, it will need to face the 7th fleet which will make the further amphibious invasion much harder.
And yes, the current China navy is not capable of doing so, and this is perfectly natural because the scale of such amphibious invasion in a such short time frame is non-precedent. They are desperately ramping up the capability of course, but it is not a that easy work. And the associated cost on the failure is pretty clear; they will lose its grip on South China sea. Taiwan re-unification is somehow political idealism-driven, but the control on South China sea is directly connected to China's national interest.