would it be possible for us to see the big bang through more powerful telescopes than james webb in the future?

We can "see" the Cosmic Microwave Background (CMB) radiation using radio-telescopes that are sensitive to "microwave" signals.

(the word "microwave" refers to the wavelength of the photons, not to the device used in the kitchen)

The first signals were finally received (and understood) in 1964.

The CMB radiation marks the moment the universe became transparent, as its average temperature dropped below 3000 K (approx. 5000 F).

Before that, when the universe was hotter, neutral atoms were impossible: as soon as an electron tried to enter into orbit around a proton, a photon of energy would come along and knock it off its orbit.

After than, when the temperature was below 3000 K, the average photon was now too weak to prevent electrons from entering orbit: neutral hydrogen was finally possible... and the universe suddenly became transparent.

The CMB radiation therefore marks the earliest moment we can "observe" with any kind of telescope that works with electromagnetic radiation (light, radio, microwave, infra-red, ultraviolet, X-rays, gamma rays...).

Having more powerful telescopes (in electromagnetic) will never allow us to go further back than the CMB radiation (still 400,000 years after the Planck Time - I suppose this is what you mean by "Big Bang"**)

Maybe it would be able to detect gravitational waves (if they exist) using a "gravitational interferometer" (there are already a few in the world, including LIGO, VIRGO). However, we are still unable to detect ANY gravitational waves -- these telescopes are not yet sensitive enough to detect anything).

The only other type of "things" that could carry information from "beyond" the CMB radiation could be neutrinos. And we can detect neutrinos... but not with any resolution. In other words, we can detect them, we can sort-of count the ones we detect, we can sort-of tell which direction they come from... and that's about it. Neutrinos are not affected by the electromagnetic force, and they interact extremely rarely with... anything. This means that they could travel through the universe as if the universe were empty... and this means they could go through our "neutrino telescopes" very easily without being detected.

IF (a mighty big if) we are ever to detect anything from "before" the CMB radiation, then it will be because we will have come up with detection devices that have nothing to do with what we now call telescopes.

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**There is no such thing as "The Big Bang". Big Bang is the name of a theory that describes the interaction between the expansion of space and the energy content of the universe.

The energy density goes down with time (same amount of energy + more space to spread it out).

The nickname Big Bang was actually given by an adversary of the theory (Fred Hoyle in 1949) and it is an awful nickname because it gives the false impression that the theory describes an explosion. It does not. It only describes the expansion of space... which is still going on.

Therefore, whenever we observe the spectrum of a distant galaxy and can distinguish the "cosmological" redshift from the other redshift effects, then we are observing the "Big Bang" (the effect of the expansion of space on the apparent distance to that distant galaxy).

This was already being done in the 1920s

After the big bang the universe was hot and dense; and opaque. About 380,000 years after the big bang, the universe had cooled enough for electrons to pair with protons, forming atoms. And then the universe became transparent. So we can never see beyond that point. We can already see this. It is called the cosmic microwave background, and appears as a nearly uniform glow of microwaves from every direction in the universe.

If we can make gravitational wave detectors, we will be able to "see" beyond this point as gravitational waves penetrated the opaque gas. But gravitational waves are weak and hard to find.

We can see it - it is the Cosmic Microwave Background Radiation.

No, because there never was a big bang. This documentary may enlighten you:

https://www.youtube.com/watch?v=IFFl9S39CTM

No