I suspect being economically strong and independent aren't enough to become a super power in today world, I realised that US is slowly losing it's grip as a super power after it starts shifting focus on other research areas and staying away from making nukes. Given today technology, can a nation become a super power without having any nuclear programme? Sorry for my childish thinking but I think people would definitely listen when you can talk at over 250dB.
That is unknown ...
Nuclear weapons have not been used in combat for almost 75 years. Their existence has loomed over geostrategic thinking, but nuclear strategy are all untested assumptions.
Once upon a time, theorists wrote papers where widespread evacuation programs were seen as more significant than localized nuclear use. Others seem to have thought roughly "any nuke is a nuke" and their very first strike would be a massive countervalue attack.
I consider it quite feasible that a major non-nuclear power could come close to superpower status using trade, cultural influence, and cyber power. Would they actually be a superpower? People would argue endlessly.
Consider virtual arsenals.
Remember how upset the US are/were about Iraqi, Iranian or North Korean nuclear weapon programs? Well, South Korea, Japan and Germany presumably have no nuclear weapon programs, but their non-existing programs are much closer to the bomb than, say, Iran. And Japan probably could overtake North Korea in a few months, if they wanted to. They are trusted not to take that step.
- They have scientists who understand nuclear weapons engineering, if only so that their national security agencies can evaluate reports of other countries' programs. They would never rely on intelligence from the P5 alone.
- They have a civilian nuclear industry with plutonium stockpiles.
- They have at least tactical delivery systems.
First to achieve Lunar/Space Colony.
Say a multibillionaire sets his sights on space exploration. Before the slow engines of states achieve similar success, his country could be lauded SuperPower if they get first De FACTO ownership of celestial bodies.
The logistical capabilities that accomplishment grants, the information available to them.
And the sheer Bragging Rights.
That makes you the sole state who controls a rare commodity, akin to China holding the Lion's share of rare earths.
Remember that Politics is the Art of looking the part.
China does have nuclear weapons, but I have never heard people citing it when arguing that China is now superpower.
They usually cite their GDP (PPP) or exports in $bn.
If that is not sufficient, consider an non-nuclear but economically powerful country with a close ally (maybe a client state of sorts) in the same military block which has some nuclear capacity but does not qualify as superpower otherwise.
Japan might be considered a super power and they don't have nukes - by choice. Should they change their stance on nukes, they could probably develop them within one or two years.
Their power is mostly through economics, technology and military Allies which are more important in todays world.
Nowadays - at least in the western world - actions are taken through trade deals and trade sanctions rather than military actions. There will be interventions if a country starts an unjustified war.
We saw this in the form of trade sanctions for Russia when they annexed Crimea. (I would like to point out that I'm not saying this was or was not justified, I am merely stating what happened - just in case I want to visit Russia in the future)
We can see how these sanctions or embargos can devastate a country in the case of Cuba or North Korea. Although they might be less effective against large countries.
There is debate within the political science community as to what defines a super power. However, a good proxy is the ability to project power.
The UK was the dominant world power during the colonial era. Few people would argue this, yet they certainly didn't have nuclear weapons. The UK could, however, blockade ports, draw on a vast empire for soldiers, and support sustained conflict anywhere on the globe.
In fact, the lack of blue water naval power is why I would not classify current day (2020) China as a superpower. ICBMs are really the only way that China can threaten countries outside of Asia. Contrast this with the current US capabilities and Cold War Era USSR power projection - either one was able to land and support troops at far removed locations.
Economic pressure is certainly a way to project power - sanctions can hurt. But I think it is insufficient.
Can the nation transport and sustain large bodies of soldiers to distant locations in the face of armed resistance?
Nuclear weapons would only play into this definition if we posit that Mutually Assured Destruction is required to prevent the other party from using Nukes to prevent landing or sustaining those troops.