What was the first political document that invoked the interest or betterment of humanity?

The Declaration of Independence of the USA is be a candidate. Although it may not be the earliest, which could be quite difficult to determine, it is arguably the first clearly political document which fulfills your requirements:

IN CONGRESS, July 4, 1776. The unanimous Declaration of the thirteen united States of America:

When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another...

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

Although the Declaration is in essence a justification and apology for the American colonies' rebellion against the British, "a substantiation for an action or a move" , it does not rely only on the particulars of the colonies' situation at that time, but conveys and invokes principles regarding "the interest or betterment of humanity as a whole". Its precepts are specifically designated as relevant not only to that particular time and place, but to the situation of Humanity at large.

The American Declaration of Independence is a declaration of independence for mankind at large, not just the Thirteen Colonies, and since it was written, it has been understood and used as such:

Abraham Lincoln, perhaps the greatest expositor of the Declaration on Thomas Jefferson, author of the Declaration:

The man who in the concrete pressure of a struggle for national independence by a single people, had the coolness, forecast, and capacity to introduce into a merely revolutionary document, an abstract truth, applicable to all men and all times, and so to embalm it there, that to-day, and in all coming days, it shall be a rebuke and a stumbling-block to the very harbingers of reappearing tyranny and oppression.

Also see: The Declaration of Independence

As a practical matter, the Declaration of Independence announced to the world the unanimous decision of the thirteen American colonies to separate themselves from Great Britain. But its true revolutionary significance—then as well as now—is the declaration of a new basis of political legitimacy in the sovereignty of the people. The Americans’ final appeal was not to any man-made decree or evolving spirit but to rights inherently possessed by all men. These rights are found in eternal “Laws of Nature and of Nature’s God.” As such, the Declaration’s meaning transcends the particulars of time and circumstances.

The tract Defensor pacis (The Defender of Peace) laid the foundations of modern doctrines of sovereignty. It was written by Marsilius of Padua (Italian: Marsiglio da Padova), an Italian medieval scholar. It appeared in 1324 and provoked a storm of controversy that lasted through the century. The context of the work lies in the political struggle between Louis IV, Holy Roman Emperor and Pope John XXII. The treatise is vehemently anticlerical. Marsilius' work was censured by Pope Benedict XII and Pope Clement VI.

Having thus defined citizen and the prevailing section of the citizens, let us return to the object proposed, namely to demonstrate that the human authority of making laws belongs only to the whole body of citizens as the prevailing part of it. . . . . Defensor Pacis

It depends on which document written by a philosopher or equivalent secular agitator was the first to be co-opted by the secular revolutionaries of Europe (or elsewhere) and hence become a political document in its own right.

Since ancient civic philosophies can become religions, Confucius' writings may not qualify as a political document in the fashion you specify.

A more modern political document would be John Locke's Two Treatises of Government in 1689.

If you mean document of this sort and written by someone in power (i.e. the government itself) then Thomas Jefferson's writings are an example.

Of course if nothing else, the League of Nations' charter would have to qualify.

As you can see, the question might be a tad broad.

Plato's "Republic" comes to mind.

Edit: as Yannis suggested, I've got two reasons why the Republic qualifies. A part of it discusses how to organize the most effective state, in what classes should its population divided into, how to organize educational system, who should take care of the kids, how to properly brainwash the populace into obedience, etc. This discussion is not tied to Athens or any other specific city-state, it's more abstract than that, therefore one can say that the proposed design applies to the Humanity as a whole.

Much later edit, in response to @LennartRegebro comments. Below is a portion of one of the dialogs from Republic that aims at justification of distinct classes in the society. Notice that the end purpose discussed how to "make the city just", not how to benefit one class or another.

"Think, now, and say whether you agree with me or not. Suppose a carpenter to be doing the business of a cobbler, or a cobbler of a carpenter; and suppose them to exchange their implements or their duties, or the same person to be doing the work of both, or whatever be the change; do you think that any great harm would result to the State?"

"Not much."

"But when the cobbler or any other man whom nature designed to be a trader, having his heart lifted up by wealth or strength or the number of his followers, or any like advantage, attempts to force his way into the class of warriors, or a warrior into that of legislators and guardians, for which he is unfitted, and either to take the implements or the duties of the other; or when one man is trader, legislator, and warrior all in one, then I think you will agree with me in saying that this interchange and this meddling of one with another is the ruin of the State."

"Most true."

"Seeing then, I said, that there are three distinct classes, any meddling of one with another, or the change of one into another, is the greatest harm to the State, and may be most justly termed evil-doing?"

"Precisely."

"And the greatest degree of evil-doing to one's own city would be termed by you injustice?"

"Certainly."

"This then is injustice; and on the other hand when the trader, the auxiliary, and the guardian each do their own business, that is justice, and will make the city just."

What about Hammurabi's Code of Laws dating to before 1750 BCE, from the Epilogue of which the following quotes are taken:

...then Anu and Bel called by name me, Hammurabi, the exalted prince, who feared God, to bring about the rule of righteousness in the land, to destroy the wicked and the evil-doers; so that the strong should not harm the weak; so that I should rule over the black-headed people like Shamash, and enlighten the land, to further the well-being of mankind.

LAWS of justice which Hammurabi, the wise king, established. A righteous law, and pious statute did he teach the land. Hammurabi, the protecting king am I. I have not withdrawn myself from the men, whom Bel gave to me, the rule over whom Marduk gave to me, I was not negligent, but I made them a peaceful abiding-place. I expounded all great difficulties, I made the light shine upon them. With the mighty weapons which Zamama and Ishtar entrusted to me, with the keen vision with which Ea endowed me, with the wisdom that Marduk gave me, I have uprooted the enemy above and below (in north and south), subdued the earth, brought prosperity to the land, guaranteed security to the inhabitants in their homes; a disturber was not permitted. The great gods have called me, I am the salvation-bearing shepherd, whose staff is straight, the good shadow that is spread over my city; on my breast I cherish the inhabitants of the land of Sumer and Akkad; in my shelter I have let them repose in peace; in my deep wisdom have I enclosed them. That the strong might not injure the weak, in order to protect the widows and orphans, I have in Babylon the city where Anu and Bel raise high their head, in E-Sagil, the Temple, whose foundations stand firm as heaven and earth, in order to bespeak justice in the land, to settle all disputes, and heal all injuries, set up these my precious words, written upon my memorial stone, before the image of me, as king of righteousness.

Of course there were earlier codes of law, as noted in Hammurabi's Code itself; but no known traces of these remain:

Yet even with this earliest set of laws, as with most things Babylonian, we find ourselves dealing with the end of things rather than the beginnings. Hammurabi's code was not really the earliest. The preceding sets of laws have disappeared, but we have found several traces of them, and Hammurabi's own code clearly implies their existence. He is but reorganizing a legal system long established.

Update: - meaning of Politics
The claim has been made that *codes of laws are not political. I offer as counter argument the definition of Politics from this source:

1.The activities associated with the governance of a country or area

No system of governance can be considered complete without a body of laws, by-laws and/or regulations that set out the scope of such governance, and the means by which it will be enacted; such is a code of laws.