This answer relies on knowledge from my answer at Does Mohs scale of mineral hardness always hold? so I suggest that you read it before you continue reading this answer.
Different materials are best for different purposes so it might not be best to create only one material to use for many purposes. For each purpose, there's a trade-off between different advantageous properties.
Given a set of properties that we want a material to have all of, there exists a an amount of each property that a material can exist with each of for which there can exist a material with even more of one of those properties but not without having less of one of the other properties.
It can sometimes be desiarable to create a single material with many purposes because it enables many different objects to be recycled together because they're all made of the same material.
Here are some possible desirable traits for such a multipurpose material: nuclear stability, infinite ductility, theoretical strength, thermal stability, reactivity, amorphous, and non-stick.
I can think of such a good material but don't know if it's stable enough to be able to be produced. Grow a perfect crystal of Carbon(IV) nitride around a seed crystal by slowly freezing it out of its molten state in an environment with a precisely controlled temperature to get rid of all impurities.
Melt it and add a small bit of excess nitrogen atoms then let it slowly cool from a very high temperature in a crucible it doesn't stick to to be stress free after it undergoes the glass transition.
I think its maximum homogeneous nucleation rate is low enough that it can undergo the glass transition because not very much volume energy would be released in the nucleation of the crystalline state because when nitrogen makes 3 bonds, its bonds can flex back and forth with ease.
Next, etch it nanosmooth with a liquid that has a contact angle greater than 90° with it. Because it has a contact angle greater than 90°, it will not stack to the object or even leave one drop on it after the last bit of the object gets pulled out so it will not evaporate from the substance redepositing what it etched away as a rough surface.
I think that as a result of the slight excess of nitrogen atoms, it will be a covalent network with random walking half antibonds and if the etching acid is dilute enough, atoms will be dissolving much faster than they're precipitating onto the surface because it's a dissolution by chemical reaction so half antibonds will random walk to the surface faster than the surface atoms get etched away giving the surface atoms a full outer shell making the material non-stick enough that the acid will not wet it and therefore leave it nanosmooth after the material gets pulled out of the acid. The material will probably have such a high theoretical strength that it's better than any infinitely ductile material that could be produced.
It will have a very high strength to start with because it was etched nanosmooth, and it will be so hard that almost nothing can scratch it very much so its strength won't reduce very much with use. A dish made of it would really truly be unbreakable as a result of its high strength. According to my answer at Why is glass so breakable?, for any material, the speed two spheres of that material that are the same size must collide with each other in order to form a crack is the sheer modulus to the power of -2 times the strength to the power of 5/2 times density to the power of -1/2 times some constant, but that substance would have a strength that's a significant fraction of its sheer modulus.
Its strength will lower even less with use because it's amorphous. Also because it's so smooth, any contact edge between water, air, and that substance will be vibrating due to the dynamic equilibruim of the water's evaporation and condensation making the advancing and receding contact angle of water with it be so close together that drops of water on plates made of that substance will roll off with ease in the dishwasher.
Even drops of a liquid that has a contact angle less than 90° but doesn't completely wet it will roll off with ease until they're at locally lowest point on the surface on the underside. Because it's amorphous, it will warp with very high temperatures so another material might be best for temperatures of 2000°C.
It's perfect crystal corundum with a small fraction of its aluminum atoms replaced with silicon atoms etched nanosmooth. Corundum actually is a covalent network according to an alternate definition despite the electronegativity difference of more than 1.7 because each bond has 2 electrons localized to that bond.
Since it's a covalent network, replacing a small fraction of the aluminum atoms with silicon atoms would create random walking half antibonds some of which would random walk to the surface making it non-stick.
I think a perfect crystal of that substance can be slowly grown from a molten mixture of aluminum, silicon, and oxygen where the amount of silicon in the mixture is very small and the number of oxygen atoms is slightly less than 1.5 times the number of aluminum atoms plus the number of silicon atoms. Actually 2 crystals would be nucleated, one of that substance and one of pure silicon. That substance could actually be etched into a crucible for molten carbon(IV) nitride because it would be so non-stick.
It would probably also be a very dark substance because it would be slightly electrically conductive. Once a research group that conducts all useful research very efficiently exists, they could actually make a giant rod of the microcrystalline version of that substance lying on the ground by pouring its molten form into a mold then freezing it from the bottom at a controlled rate by laser cooling the part just under the freezing surface then chiseling it into an elevated railway.
That railway would only weather at the surface because it would be nonporous because grains wouldn't detach from other grains anywhere on their surface because the grain boundaries wouldn't be under very much stress because atoms could move across the grain boundary to release the stress caused by the different grains contracting more in a different direction because all grains are the same substance.
I think it should be considered a type of rock because it's a hard, opaque, brittle, nonshiny solid. Water could not go in and freeze cracking it.
Buildings could also be made from that material and be strong enough to support themselves and even withstand an earthquake as long as there's no sharp concave edge in them and they would also be fireproof.
Lonsdalite could in theory be much more unbreakable under the right conditions. Suppose you have a sheet of it parallel to its own cleavage plane made by fracturing it along its cleavage plane.
I think it will retain it's extremely high theoretical tensile strength even after scratching because if it goes under tension after it gets scratched, the tip of the initiated crack will propagate parallel to the surface rather than propagate further in.
If the lonsdalite had a small impurity of nitrogen atoms in it, the brittle fractured surface would also be very non-stick and low friction and since it also has a high thermal conductivity, no part of its surface would heat up very much from scratching and since it's low friction and doesn't easily heat up from scratching, it would be really slow to get scratched retaining its theoretical strength as it gets scratched.
That property is an orientation dependent property so it would not be possible to build an object out of it of any shape and have it be so unbreakable.