The idea that the outbreak originated from a Chinese attempt to weaponize the virus seems plausible, but I think it's less likely to be the Chinese government itself, but rather elements within it who are responsible. I think this scenario fits better with Max Brooks' focus on political realism, and theme of system failure.

So, we might imagine, hawkish elements within the PLA, (who have always had a difficult and contentious relationship with Politburo), embarking on a clandestine bio-weapons program to defend against the American threat.

My evidence:

1) The fact that something went wrong within the research facility, and an outbreak occurred at all, points to sub-standard lab practices, which are more likely in an ad hoc research environment, than a purpose built lab.

2) The failure of the Chinese government to contain an outbreak, and an atmosphere in which it seems the special response unit is playing catchup, suggests that there is no prepared contingency for an outbreak, something which would exist in an officially sanctioned weapons program.

3) The flooding of the area, in which the "moondiver" contracts the virus, seems like exactly the sort of thing one would do, in order to clandestinely destroy an underground laboratory complex. This action is clearly directed at the destruction of evidence, more than the containment or elimination of the virus. Why would the government need to destroy evidence of a sanctioned weapons program? They wouldn't. However, learning that an element of the PLA had embarked on an unsanctioned bio-weapons program is a secret that has to be protected. First, news of this kind of open sedition would greatly damage the central government's ability to rule, and just as importantly, this action would be seen as a direct threat to the US.

TLDR; my theory is that hawkish group of PLA officers were attempting to clandestinely weaponize the virus, without the approval of the Beijing government. Something went wrong, and the virus had already begun to spread by the time the central government learned what was going on, and attempted to contain it.