With regards to
Which distributions were the first and when did these projects start?
This is discussed at the beginning of Glyn Moody's book "Rebel Code", in Chapter 6, "Boot Then Root".
He mentions the distribution from MCC (the Manchester Computing Center) as being a very early example, though perhaps not the first. However, the book does not mention an earlier example.
The First MCC Interim version, using the 0.12 kernel, appeared in February 1992.
He then says
As the MCC Readme notes, "Very shortly after the first MMC Interim version of Linux appeared, other people released similar versions: Dave Safford's TAMU [Texas A&M University] releases, and Martin Junius's MJ Versions were eventually followed by Peter MacDonald's massive, comprehensive SLS releases and H. J. Lu's small base systems."
The SLS (Softlanding Linux System) was an important early distribution.
Debian is generally considered an immediate successor of SLS, and Debian's founder, Ian Murdoch said at the time that SLS was "possibly the most bug-ridden and badly maintained Linux distribution available; unfortunately it also [sic] quite possibly the most popular".
Both Slackware and Debian began in 1993. So the distributions mentioned above, none of which exist any more, could be considered the first wave before the distributions we know and love made their first appearance.
I am not sure if
How did people have the idea Linux would work better with a distribution and start the first distribution(s)?
has a clear answer. It is clear that not everybody can build their own distribution from scratch, any more than everybody can build their own automobile.