No. You need a properly organized central government with the right resources and the right policies. The Song lacked the right policies. That's it.
A properly organized government with the right policies and resources is a start. But that doesnt get you an industrial revolution anymore than wood and gasoline gets you a fire without a match and a person to light the match.
The textile industry lead the revolution in England because the middle class had enough disposable income to want to buy nicer clothes in volume. No disposable income/no need to mass produce textiles. Second, you need someone to appreciate the need for higher volume production. Why would a centralized government be so attuned to the whims of a middle class merchant? It's a long shot without private, individual initiative.
The exceptions to this might have been military weaponry or major, pyramidesque type projects. Perhaps an individual, keen to gain favor from higher ups could "industrialize" various processes. But, these endeavors usually have a limited lifespan - make a 100,000 swords and a million arrows for a campaign and you're done. It's too easy to draft the people and resources for one off issues, particularly with powerful monarchies and empires. Hence why neither of these efforts led to industrialization by the Chinese, Romans, Arabs, or anyone else.
I might be underestimating value of coal furnaces as a spark for the industrial revolution. But I have generally found that technological advances such as the ones made during the initial stages of the industrial revolution typically come from solving a problem (necessity is the mother of invention) rather than the reverse - develop the technology and then find ways to use it.