Would they be neutral, or would the NAM become a third bloc in the Cold War, as they would now be grouped around a superpower who would probably jump to defend other "Neutral" members.
IMO, Brazil is really the only country isolated enough to not pick a side yet strong enough (with a few good generations) to stand up to Russia or America; although they would be the weakest of the Superpowers I think being a super power makes you not able to be Neutral.
Actually, a NAM Superpower more than anything else. They'd be a country with an sphere of influence and loyal countries in a NATO arrangement, however, the country would move out as soon as the US and USSR engaged in war over a country.
Britain does not lose her empire, fares better econimically and during the cold war is concentrated on maintaining her empire against the uncultured capitalists and barbaric communists.
Or.
Union of Anglo-French Empires.
Or.
Nazi Germany survives until the cold war.
Or.
Japan picks better targets and get more lucky, does not start war against US, keeps
his empire.
Or.
Early succesful chinese industrialisation attempts with foreign support and with someone else than communists winning civil war.
Or.
Italy bets on the winner in all wars and attains Mare Nostrum
Japan is male, not female.
That said, I thought more on Canada undergoing a demographic explosion of sorts and declaring full independence from the UK earlier, as well as becoming the leading power of the Commonwealth.
Prospective states and (their problems):
Sukarnoist Indonesia (not well-liked by certain neighbours. Too geographically close to the West, namely Australia. Not great power-projection capability, or resources aside from minor oil and rubber reserves and labour. Fairly reliant on Western markets).
Brazil (not powerful until relatively recently, located in an area of heavy US-interference. Lack of linguistic or historical ties with Hispanophone neighbours. Consistently underperforming).
India (massive internal issues, consistently outclassed by China. Too many hostile states too close by and not enough nearby 'allied' states to easily project power/defensive capacity to. Dysfunctional governmental system).
Lumumbaist DR Congo (little access to the ocean, poor infrastructure, major internal divisions, likely to have a purely African focus).
South Africa (internal divisions, poor image, relatively isolated geographically, military largely unsuitable for power-projection).
Yugoslavia (strong, but not capable of good power projection. Squashed it its own neighbourhood between Eastern and Western blocs).
It seems that to be a superpower during the Cold War you need a) a strong ideological basis (probably anti-colonialism and autonomy), b) a very large economy with advanced tech (to provide as aid and incentivise alliance and c) an effective nuclear umbrella, with the capacity to hit any target on Earth with a large number of ICBMs.
In this case, the ideological basis would be heavy anti-interventionism and mutual protection.
A Third Superpower must have a different ideology that is neither capitalist nor communist; and it must contradict the two.
Or simply one whose ideology is to not allow either Superpower to threaten the independence of those within it's area of influence.
Or an entire realignment of the cold war idelogical war. Various levels of centralization could be the argument. Dicator vs democracy, or even religious lines could be used. Either way if their is a Third power they will have their own interests and in those interests they would seek a way of self justification distinct from the others.
Though I will argue that under realist thought a tri-polar world would probably collapse on itself to either a duo-polor, or a mono-polar system
I think you're overthinking it. I'm not making an ideological Superpower as much as I'm attempting to make a "country powerful enough to hold the US and USSR back, run a democratic mixed economy, and keep the US or USSR away from lands disputed between groups". It'd be a country who would launch a military intervention in Korea to push back North Korean forces, but would send US forces back to where they came from and wouldn't attempt to push deeper into NK.
Alternatively, think of a country that enter the Vietnam war supporting a joint government and pushes Soviet and American troops away from the North South border and sits there to make sure neither attempts to cross.
If a country is unwilling or unable to protect power over a wide area, it can't really be a superpower. A neutral power might not be willing to do so, regardless of its economic or military strength.
It is willing, but only if one of either existent Superpowers attempts to set up an ally over there and ignore that country's right to self determination.
This is, by definition, impossible.
1) to be a Superpower, not just a Great Power, you need to be one of 2 (arguably 3) powers in the world. None of those powers can be 'neutral'. Sure A can be neutral between B & C, but A will have issues with B and with C, so can't be considered neutral.
2) you don't rise to the level of being one of the 2 or 3 top world powers without growing and expanding, and developing a power base. Once you do that, you're not 'neutral'.
A neutral Great Power? Maybe. The US was that w.r.t. Europe. Although Mexico, Hawaii, all of the Caribbean and much of South America would find it hard to call the US 'neutral' with a straight face.
Then it wouldn't be neutral, but "as close to neutrality as possible". This Superpower would simply prevent any of the two countries from attempting to invade or support a dictatorship allied to them, instead making sure an independent country ran itself as it saw fit and choose whichever alignment it desired without intervention.
Basically, if Allende came to power and the US backed his coup, this superpower would initiate an armed intervention in Chile to depose Pinochet and restore Allende or his government. If the USSR attempted to take over the Baltic, this power would push them back and keep itself there to make sure they wouldn't go in, but respect the decision of the Baltic countries.
As for candidates, Canada, Mexico and Brazil do come to mind. Basically, their ideology would be virulent anti-imperialism from either side of the Cold War. Think of them as a shield for smaller countries caught in the crossfire of the Cold War and this Superpower as a wall that stops them from meddling in their affairs. If they pick to join the US or USSR, then this power would let them, but it wouldn't let the US or the USSR from making them pick under duress.