There is no question that if China wants to build more ships than US, it surely can be done. However, whether that will happen or not depends on future China's global military policy.
US is struggling financially with the available numbers of ships in order to maintain their global military dominance, they need their allies to assist them by sending ships from Europe, Canada, Australia and Japan. US can not do it alone without causing economic hardship in their homeland, as seen in the Gulf wars, Syria, Afghanistan and Iraq. They need their NATO allies to pour in money and military assets.
Therefore, unless US economy improves beyond current rates, they will not be willing to add significant number of navy ships, the Pentagon will have to face approvals from the President, the Congress and the Senate.
On the other side, there is no reason for China to assume the role of global police, and with the current non-interference policy, the expansion of China navy is basically aimed at waters surrounding China, the main aims are to deter US attacks on Chinese coasts, to re-unify Taiwan, to protect shipping routes for goods flowing in and out of Chinese ports.
For these aims, there is no need to build more ships than USA but rather to build sufficient numbers to counter what can be mobilised by USA and its allies to deployed ships near Chinese coast lines, and along the shipping routes for Chinese imports and exports.
US doctrine of 1 ship on deployment, 1 ship on standby and I ship in maintenance means that only 2/3 of their ships are available, and they cannot move all their available ships to China's coasts because that will leave vacuum in other parts of the world like Atlantic, Middle East, Indian Ocean, Baltic sea etc.
China does not need to maintain US style of "1 ship deploy, 1 ship on standby and 1 ship under maintenance" because their ships are not send for long endurance global policing patrols. They can easily maintain a "more than 4 ships deployed and I ship under maintenance" as seen on their deployment of all three type 071 LPD during the search of missing MH370 in 2014 (the 4th type 071 was commissioned in 2016).
In short, China is unlikely to build more ships than USA, unless a war break out or a war with USA is unavoidable. But they do have the industrial power that match if not more superior to US ship building industry.