Sure...China could invade the ME...if it wants to eat that turd it can. Go through India? Nah, that ain't gonna work well. Those moves are really just equivalents to 'death by cop'.
Australia and the rest of the Pacific Islands...How in the hell is China going to transport the troops to get to Australia. Almost ALL of their amphibious lift capacity is civilian, slow, ungainly, and not suited to the sort of voyages needed for Australia. All that tonnage is gonna get sunk pretty dang easily, and their Navy wouldn't be able to really protect them.
As for Korea...at this point, we can let the RoK deal with the Norks by themselves, with the assistance of whatever assets are already on the peninsula.
What you're discussing here is really just a form of suicide by the Chinese that will make sure they are isolated from the rest of the world.
Well, Russia and Iran are the obvious ones. Pakistan is also a potentially useful staging area, though likely to just move troops into Iran, or naval operations into the Indian Ocean. India I guess could have some say in the matter if they invaded and tried to conquer Pakistan, but there are some obvious reasons India wouldn't like to do that.
A lot of the middle eastern countries don't particularly love us anyways, and especially won't love us when were effectively blockading them. UAE already is making a lot of independent moves. Russia currently is the one with basing, though in such a big move/showdown as this, I'm pretty sure Russia would gladly allow Chinese use of their bases, and joint exercises are already done with Iran.
Other options are perfectly available in a scenario where China isn't suprised by the war: China apparently has roughly 60 million veterans, due to the short conscript time, so swelling the army by several million is quite doable in 6 or so months. If committed to war they could recognize the Yemen government and secure basing rights there, pre-positioning a 100k+ or so troops there. They already have a base in Africa, and could also simply chose a side in one of Africa's many civil wars and secure basing for several thousand more troops. There are also apparently several million Chinese nationals in Africa, and China does have private secuirty forces there (as well as Russia's various operations still kicking around) so in lead up to war those could likely be substantially reinforced, how substantially and how quietly dependent on local conditions.
So, I'm pretty sure securing basing in Iran, Russia, and Syria are more or less givens. Other basing could be found in Africa easily enough, depending on the window basing was needed and the political peculiarities of the situation. Yemen, Somalia, Sudan, and Libya a likely options for basing, due to local political conditions being fractured, too weak to say no if the Chinese just start setting up shop and building bases, and in strategically valuable locations. Moving into those locations probably triggers a ticking clock though, so can't really be done except as building up to war.
Getting half a million Chinese troops into the middle East isn't that big of an ask compared to existing Chinese logistical capacity and options in the area: a one lane road can move about 1,000 people an hour fairly easily, so even if you had to move 500,000 by a single road, that only takes roughly 500 hours, or 20 days. Moving the army in peacetime there's way more transport capacity, and even in an embargo situation, there are way more than a single road to move men and material down.
So, African campaign could be some 500,000 Chinese, probably not super heavily equipped, but a good amount can be pre-positioned, and over time more material can be moved in, roughly 100,000 Syrian army, who at the very least can help deplete enemies guided munition stocks, Iran has about 1 million troops, who generally seem to above general Arab quality, given performance in the Iran-Iraq War.
In War, Syria and Iran can be used to push and overun Kurdish positions and the Americans in support, the only group I'd have any confidence will fight for America without massive American support. Some elements of Iraq might fight for America, especially to stop Iranian invasion, but a lot also won't, and might even fight in support of an Iranian invasion.
All the nations along the Persian gulf probably won't fight for the US unless there is a large American presence to force them to do so, and are probably just as likely to red wedding the current small American forces there. I think there's roughly 50,000 US troops in the middle East right now, spread out mostly in logistical bases.
One properly equipped group army (Chinese corp sized formation, 30-50k could probably roll out of Iran into Kuwait and sweep the Americans out the gulf sea in not much more time than it takes to drive there at a leisurely pace, 1-2 weeks. or or specifically, for the formation to drive down, order the Americans to surrender, and if they don't place a land blockade and have the Iranians mine the US harbors so they can be sieged out relatively safely.
Assuming the US didn't react at all. Which is not a reasonable assumption. If a Chinese Army is in Iran, plus whatever extra naval and air weapons they want to bring in for "exercises", and another army group is put in Syria for peacekeeping, and another in Sudan or Somalia for peacekeeping, the US is going to have to do to something, especially if they're planning to do something as dramatic as a general blockade.
Still, for relatively cheap it dramatically increases American escalatory risk, and if combat does break out likely produces if nothing else a black hole to attrition away Blue men and material. And a Chinese army in the area is going to upend various players in the regions calculations too. Probably in unpredictable ways.
Turkey's probably the big swing question here. If they stick with NATO, its a large army, and while fighting it is still probably a net plus as a sink of Blue material, it would be better to be killing Americans manning American weapondry, rather than Turks with American weapondry. It also would draw focus North, which might be to Iran, Syria, and Russia's benifit, and might be especially benifitical to Armenia, but would not be in China's interest, who care more about the Persian gulf and Red sea. If Aserbiazian needed to be crushed to secure Russian-Iran supply lines, or Turkey needed to be gutted by forming a Kurdishtan, that's much more a second year of the war priority than a first year one.
If Turkey joins in stomping the Kurds but is otherwise neutral, that secures the flank of the operation, dramatically limits available NATO forces in the area, and generally makes any NATO operation into the middle east less secure, because NATO might fully flip sides. Forcing a lot of virtual attrition as Blue has to keep forces in reserves in case Turkey does something.
And if Turkey flips and decides to Join China and Russia's campaign of seizing clay that's rightfully yours, and sees how much fight there is left in the Greeks, NATO would be in a very bad position.