>>17807713 (OP)
Here is my best understanding of what I think to be the most important reasons, although there are a multitude of underlying factors behind this particular group ending up as the permanent members.
First, all five of these countries were very assertive in insisting they should be on the UNSC when it was founded. There were others who advocated for their entry as well -- but they were excluded for reasons explained below.
Second, these five countries all did not want there to be too many countries in it. All five countries wanted it to be a small number of permanent members. For example China wanted to specifically make sure they were in it and countries like Japan were not, so that they could feel better about themselves. This was a major motivation for those countries why they originally went along with it.
Third, regarding the inclusion of US, UK and France: the countries of the free world did not want to be represented by only one nation in the UNSC. The representatives of the US, UK and France also liked the idea that they would constitute the majority of the council (three out of five), although this doesn't matter as much as it might seem, since all it takes is one member to veto any motion. Still there is a certain intangible psychological effect that remains from this. In particular also, the UK in 1945 had not entered its collapsed state (and the Suez Crisis had not happened yet), and was still perceived as a superpower, so in some ways this balance is an artifact of the time in which the council was created. Since the UN was created in 1945 (before countries like India existed) this part of it has pretty much been locked in stone. To change it would seem to threaten the foundation of the UN itself, thus has not been seriously attempted.
To soften the perception of exclusion, the UN allows for there to be "rotating members" of the UNSC as a kind of compensation so it doesn't look as exclusionary as it otherwise would, even though it still is.
