When was the first FPTP election, and which group/person dreamt it up?
It's quite difficult to pin down in the historical record when first past the post was first-ever used as a system for historical elections, because it's a fairly intuitive concept: the idea of the candidate with the most votes being elected to a position of leadership or to act as a representative, even if they have less than half the votes, is a straight-forward concept. Many of the more complex, alternative voting systems that we are familiar with today are a consequence of the development of modern political parties in the 19th and 20th century. The majority of countries that use first past the post today probably take inspiration, directly or indirectly, from its use to elect members to serve in the United Kingdom's House of Commons.
In terms of the legal history of first past the post as a 'modern' voting system, the oldest surviving election returns for the English parliament we have date from the 1270s - but at this time Parliament as an institution did not exist in the same way that we understand it today, and election returns simply advised the Crown of who had been chosen to serve, not how they had been chosen. The oldest reference I am aware of to mandating the use of a specific voting system comes from 1430: a law governing the franchise passed in that year also provides us with the first legal reference to election by "the greater number" of voters. This most probably represented a codification of existing practice rather than a change in the electoral system, given the limited options for selecting representatives at this time, but would appear to be the origin of first past the post in formal legislation.
But elections in medieval and early modern England were a very different beast to modern elections. For much of England's parliamentary history, elections to the House of Commons were not very often contested - it was much more likely that sole candidates would be agreed in advance by powerful elites, and the electoral system was filled with opportunities for corruption. Elections were not about representing the interests of the population as a whole as much as they were finding champions of different groups within the ruling elite of a given time period. When elections were contested, the number of people who could vote was highly limited until the 19th century, and the odds of there being more than two candidates in a poll were slim indeed in any given contest. This was also a time before ballot papers were printed in advance of the election. By the 17th century it was normal practice for elections to be decided first by a voice vote and then, if it was not clear which side had the most votes, by a visual estimate of how many people there were supporting each candidate. Only after this would a headcount be resorted to.
As the number of contested seats in elections increased and voting became more and more of a public spectacle, this could become a problem for the authorities in identifying a winner. Just because one candidate had the largest mass of people didn't mean that he had the largest number of eligible voters behind him; in the 1624 election for the English House of Commons, the result for Cambridgeshire had to be annulled and the election re-ran when it emerged that the local official responsible for conducting the poll may not have taken the time to report a proper result. In the 17th century this prompted recommendations from some parliamentarians that voters should actually be counted as a matter of course, but their proposals would not become law for some time. Interestingly, the House of Commons in the UK still votes this way today: first by voice vote, and then (for any vote that isn't near-unaminous) by physically standing in a voting chamber, where a volunteer from your side (always 'aye' or 'noe') counts the number of people and reports back to the Speaker of the House. If you enter the wrong voting lobby, you have to rush to the other one to be counted twice and thus cancel out your own incorrect vote!
There were also inconsistencies in deciding how to elect multiple members to represent a single constituency. Strictly speaking, under modern day interpretations of first past the post, you have one vote for each position up for election in a constituency - if there are two seats up for grabs, you have two votes. This was not always the case in the many multi-member constituencies that existed in the early modern parliaments, however. At the discretion of local officials, some constituencies would elect two representatives via a single contest with the most popular two candidates being elected; others would hold two ballots, electing one person first and then another in a second contest. The way in which first past the post was applied was thus inconsistent across the country for much of the country's electoral history, and electoral practices would not be reasonably well standardised until the 19th century. Even then, electoral arrangements for much of the 19th century were still quite different to modern ones - single-member constituencies were not the norm until the 1884 Reform Act was passed, reducing the number of multi-member constituencies to just two dozen from well more than two-hundred after the 1832 Reform Act.
In North America, the widespread use of first past the post in elections has its origins in the very early colonial period. Legislatures were established with elected representatives in Virginia and Bermuda in 1619 and 1620, respectively. Though we don't know for certain how the early Virginian legislature was chosen, we know the elections in Bermuda in 1620 were held using first past the post, although the vote then was made by voice alone. Bermuda has now been using first past the post for its elections for almost 400 years. As for Virginia, we find that that in 1646 electoral law clearly states that the selection of representatives to the colonial legislature is by a "plurality of voices", and it is very likely that - following the example of Bermuda - first past the post was always the system in use.
It is worth pointing out that terms like 'majority' and 'the greater number' can be confusing to modern readers. Particularly in the United States, it is common to think of 'the majority' as meaning 'more than half plus one' - but this has not always been the case. If we trace the history of Virginian electoral representation, we find that laws vary in how they describe first past the post. Legislation in 1646 and 1705 provides for elections to be determined by "plurality of voices" and "the most votes" (1705), but other laws make reference to "the major part" (1655) and the "majority of the freeholders" (1699). This seems particularly confusing in light of the fact that the US Constitution uses the term 'majority' to refer to half plus one in deciding the outcome of an Electoral College vote. The reality is that the definition of 'majority' in the context of electoral law has always been a little flexible, and is often used interchangeably with 'plurality' in the English-speaking world. To this day in the UK, a candidate who wins an FPTP election 40% to 30% is described as having a 'majority' of 10% over the runner-up. Legislation passed in the 19th century to extend first past the post voting by the enfranchised public as the method of election for the House of Commons uses the term 'majority' where a modern American reader might use 'plurality'.
So identifying the origin of first past the post as we understand the system today isn't very straight forward. As a method of group decision-making, it is fairly intuitive to come to - but then other options are possible (like two-round systems or more consensus-orientated ways of agreeing selection). The sentiment that the plurality of voters should support a candidate appears to have been recognised in law in the early 15th century, and was certainly so well entrenched in British electoral culture that in the early 17th century that it was being reproduced from the outset in the emerging local legislatures of its colonial possessions.