Is the time value of money natural or artificial? Certainly there is a time value of money: If the nominal interest rate of treasury bonds is 5%, then if one has a choice between receiving a hundred dollar bill now and receiving it a year from now, the better option would be to receive it now.

But what if we lived in a society where charging interest is illegal? Would there still be a time value of money? In other words, if we lived in such a society, then if one had a choice between receiving a hundred dollar bill now and receiving it a year from now, would the better option still be to receive it now?

So the essence of my question is "Is the time value of money natural or artificial?" If it is natural, then a law against charging interest would have no effect on the reality that there is a time value of money. And if it is artificial, then the law which states whether charging interest is illegal or not is what determines whether there is a time value of money.
Let's first write down two realistic reasons as to why the "time value of wealth" (since here "money" is considered in its function as store of value), is "natural and not artificial", to use the OP's words.

1) The phenomenon of inflation. If we expect to see price inflation, then a given amount of nominal "wealth tomorrow" will buy for us less goods and services than the same amount of "wealth today". So "wealth today" is preferable than "wealth tomorrow", since what we care about, is goods and services which are the things generating utility for us.

But note that inflation is not some always-present phenomenon in all economic systems, economies, countries, eras: for example the 19th century has been largely a deflationary period, with prices tending to fall during the century, in the main capitalistic economies.

2) The uncertainty of the future. This is always present, even if it has to do with the possibility of unexpected death. So "wealth tomorrow" may not be enjoyed because I will have die suddenly and unexpectedly till then. So "wealth today" is preferable, and so more valuable.

In a lending and borrowing situation, we can also map to the "uncertainty of the future" the risk of not-repayment etc. and so view the time value of wealth as being also a compensation for undertaking these risks.

Also, in a long-term approach, eventually we all die, so the very finiteness of our horizon creates a situation where "wealth today" is more preferable and so more valuable than "wealth tomorrow", if this "tomorrow" is far in the future.  

The thing is, economists argue that "wealth today" is always preferable to "wealth tomorrow"
a) even if there is no inflation, or alternatively, if we examine wealth in "real terms" (i.e. in terms of goods and services),
b) even if there is no uncertainty at all,
c) even if we have an "infinite" time horizon, i.e. even in the hypothetical situation that we are certain that we will never die, not even from "natural causes."

This is why in intertemporal models of consumer choice and utility optimization that are deterministic /incorporate no uncertainty, and assume an infinite time horizon, still, a "discount factor" exists that discounts future certain utility in real terms, which indirectly reflects that "wealth today" is preferable to "wealth tomorrow".

What is the argument behind that? Well, sometimes there is no philosophical argument only a methodological argument: "a deterministic economic model with infinite time horizon and in real terms is an approximation to reality, which is uncertain and has finite horizon for economic agents, and so we include the discount factor to keep it a little closer to reality". That's fine, that's what economic models do (models in general actually).  

But could we come up with an argument that even an immortal living in a perfectly deterministic world, would prefer "wealth today" to "wealth tomorrow"?

We can. It's called "opportunity cost". It can stand on its own without invoking uncertainty or the possibility of death. It depends on the following very simple axiom, which is supported by timeless experience related to human behavior: "more is better". Under this axiom, having wealth today will permit me, if I choose so to have more wealth tomorrow and for all tomorrows. So it potentially expands my "choice set" for all eternity.  If more is better, then I want a larger choice set, so I would prefer to have all my future wealth today rather than tomorrow.

...one could of course argue that the "more is better" postulate is not an independent trait of humans, but is one more incarnation of the "survival instinct" and so it is in reality a response to uncertainty and risk of death. Certainly, but everything can be eventually attributed to the "survival instinct", and what explains everything explains nothing.