Question: 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.

Answer: 
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.
Power Projection
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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.

China Today
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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.

Soft Power
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Economic pressure is certainly a way to project power - sanctions can hurt. But I think it is insufficient.

Bottom Line
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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.