While more can always be said, this question has come up quite a number of times recently.

This answer by /u/indyobserver probably gives the most thorough rundown of what happened at the Constitutional Convention that led to it. The brief summary in that answer:

...yes, there was some conscious thought in giving smaller states some advantages, but that decision was more or less designed to be in line with the general compromises that had developed elsewhere during the Convention than anything particular to the selection of a President. In addition, the Founders were badly wrong in their guesses on how elections would work in practice, and their inability to predict this nearly blew up the nascent United States in 1800 and has plagued the electoral process ever since.

This answer from /u/jelvinjs7 says much the same thing:

I think it's an error to say that it was really designed to do anything in particular. To quote historian John Roche, “The Framers did not in their wisdom endow the United States with a College of Cardinals—the electoral college was neither an exercise in applied Platonism nor an experiment in indirect government. It was merely a jerry-rigged improvisation which has subsequently been endowed with high theoretical content.”

This answer by /u/uncovered-history, however, gives a slightly different take:

The Founders designed the system using the Electoral College because they had little faith that the Masses would consistently want the right person as president, so they created a system that could bypass democracy to instill leaders that the political elites approved of.

In this answer provided by AvTheMarsupial, they say there is "a little" truth to the angle that the Constitutional Convention delegates distrusted the masses, and also that there was also "a little" truth that it was designed to protect the small states from being dominated by the politics of larger states, but adds that there was another more direct reason:

Instead, the Framers were more worried that the Legislature would have influence over the Executive, and that the Federal Government, while still being elected by the People, would be dominated by the Legislature.

That user then gives a useful breakdown of the debates at the Convention, what was considered, and how it led to the Electoral College.

In a previous post of mine, I linked to several of these answers above and also pointed out that it's also important to recognize that the Electoral College was criticized from the very start. Indyobserver's answer above essentially says the same thing, adding that it "nearly blew up the nascent United States in 1800 and has plagued the electoral process ever since". If it was designed to do anything in particular, then whatever it was, opponents believed it thwarted the American ideal of democracy, so the more democratic-minded politicians of the United States' earliest years did work to make it less powerful, after the debacle of the 1800 election. That may not have worked out in practice. Nevertheless, whatever its intention, the Electoral College has had its critics since the beginning, so it would be wrong to believe that the political elites of the time were all of one mind on the issue.

I suggest you check out this [answer] (https://www.reddit.com/r/AskHistorians/comments/hmf0vb/why_was_the_electoral_college_established_instead/) by u/lord_mayor_of_reddit which links several answers to variants of your question as well as providing some insight in the post itself. well, nevermind.

I'll add my answer directly to your questions anywho.

Do we have any primary sources establishing the purpose of the electoral college?

Yes, [Federalist # 68] (https://avalon.law.yale.edu/18th_century/fed68.asp) covers it and is the starting point to determining why it exists per the words of the founders (well, a founder).

What was the Founders' purpose in creating the Electoral College?

Oh, I'm glad you asked. We've gotta put our back in time goggles on, because what we have just didnt really exist so there was no real precedent. There were some historic governments somewhat similar, but our founders studied a great many of them and didn't find a blueprint they found to be "more perfect" (seriously, Jefferson sent trunks of books back from France in the 1780s for anyone who wanted them. Madison did want some and so recieved a ton, which he then studied extensively to formulate a plan we now call the Constitution). How did it happen in a parliamentary style government? The legislative body would vote for the executive, and it was usually from amongst their own ranks. In fact Benjamin Franklin's Articles of Confederation from 1775 stated that;

An executive Council shall be appointed by the Congress out of their own Body, consisting of 12 Persons...

It didn't happen but it does show what the prevailing historic trend, particularly for British colonies being run by lawyers trained in British law, were thinking (Franklin certainly was no lawyer, however many were - Jefferson, Adams, Jay, Hamilton, Madison, Monroe, Wythe, Edmund Randolph and his father John and uncle Peyton, Patrick Henry, etc, etc). A bunch thought that was a bad idea, and compromise became the order of the day.

So what does 68 say? I posted a good bit of it in reference to a question about why we didn't go the parliamentary route a while ago, the relevant bit being posted below.

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Question one - why didnt we enact a parliamentary system of executive? Federalist 68-73 deal with the executive, and 68 gives a good bit of logic as to why;

THE mode of appointment of the Chief Magistrate of the United States is almost the only part of the system, of any consequence, which has escaped without severe censure, or which has received the slightest mark of approbation from its opponents. The most plausible of these, who has appeared in print, has even deigned to admit that the election of the President is pretty well guarded. I venture somewhat further, and hesitate not to affirm, that if the manner of it be not perfect, it is at least excellent. It unites in an eminent degree all the advantages, the union of which was to be wished for.

It was desirable that the sense of the people should operate in the choice of the person to whom so important a trust was to be confided. This end will be answered by committing the right of making it, not to any preestablished body, but to men chosen by the people for the special purpose, and at the particular conjuncture.

It was equally desirable, that the immediate election should be made by men most capable of analyzing the qualities adapted to the station, and acting under circumstances favorable to deliberation, and to a judicious combination of all the reasons and inducements which were proper to govern their choice. A small number of persons, selected by their fellow-citizens from the general mass, will be most likely to possess the information and discernment requisite to such complicated investigations.

It was also peculiarly desirable to afford as little opportunity as possible to tumult and disorder. This evil was not least to be dreaded in the election of a magistrate, who was to have so important an agency in the administration of the government as the President of the United States. But the precautions which have been so happily concerted in the system under consideration, promise an effectual security against this mischief. The choice of SEVERAL, to form an intermediate body of electors, will be much less apt to convulse the community with any extraordinary or violent movements, than the choice of ONE who was himself to be the final object of the public wishes. And as the electors, chosen in each State, are to assemble and vote in the State in which they are chosen, this detached and divided situation will expose them much less to heats and ferments, which might be communicated from them to the people, than if they were all to be convened at one time, in one place.

Nothing was more to be desired than that every practicable obstacle should be opposed to cabal, intrigue, and corruption. These most deadly adversaries of republican government might naturally have been expected to make their approaches from more than one querter, but chiefly from the desire in foreign powers to gain an improper ascendant in our councils. How could they better gratify this, than by raising a creature of their own to the chief magistracy of the Union? But the convention have guarded against all danger of this sort, with the most provident and judicious attention. They have not made the appointment of the President to depend on any preexisting bodies of men, who might be tampered with beforehand to prostitute their votes; but they have referred it in the first instance to an immediate act of the people of America, to be exerted in the choice of persons for the temporary and sole purpose of making the appointment. And they have excluded from eligibility to this trust, all those who from situation might be suspected of too great devotion to the President in office. No senator, representative, or other person holding a place of trust or profit under the United States, can be of the numbers of the electors. Thus without corrupting the body of the people, the immediate agents in the election will at least enter upon the task free from any sinister bias. Their transient existence, and their detached situation, already taken notice of, afford a satisfactory prospect of their continuing so, to the conclusion of it. The business of corruption, when it is to embrace so considerable a number of men, requires time as well as means. Nor would it be found easy suddenly to embark them, dispersed as they would be over thirteen States, in any combinations founded upon motives, which though they could not properly be denominated corrupt, might yet be of a nature to mislead them from their duty.

Another and no less important desideratum was, that the Executive should be independent for his continuance in office on all but the people themselves. He might otherwise be tempted to sacrifice his duty to his complaisance for those whose favor was necessary to the duration of his official consequence. This advantage will also be secured, by making his re-election to depend on a special body of representatives, deputed by the society for the single purpose of making the important choice.

Hamilton's saying if we let "parliament" decide who is in charge without a system to check it, the office will be corruptable. They also didnt want an uninformed vote, so they came up with another way to do it. We call that way the Electoral College, and 68 also speaks plainly to that.