  Many aspects concerning the formation of spiral and disc galaxies remain
unresolved, despite their discovery and detailed study over the past $150$
years. As such, we present the results of an observational search for
proto-spiral galaxies and their earliest formation, including the discovery of
a significant population of spiral-like and clumpy galaxies at $z>1$ in deep
\textit{Hubble Space Telescope} CANDELS imaging. We carry out a detailed
analysis of this population, characterising their number density evolution,
masses, star formation rates and sizes. Overall, we find a surprisingly high
overall number density of massive $M_{*} >10^{10}\mathrm{M}_{\odot}$
spiral-like galaxies (including clumpy spirals) at $z > 1$ of $0.18\,{\rm
per}\, \mathrm{arcmin}^{-2}$. We measure and characterise the decline in the
number of these systems at higher redshift using simulations to correct for
redshift effects in identifications, finding that the true fraction of
spiral-like galaxies grows at lower redshifts as $\sim$ $(1+z)^{-1.1}$. This is
such that the absolute numbers of spirals increases by a factor of $\sim 10$
between $z = 2.5$ and $z = 0.5$. We also demonstrate that these spiral-like
systems have large sizes at $z>2$, and high star formation rates, above the
main-sequence, These galaxies represent a major mode of galaxy formation in the
early universe, perhaps driven by the spiral structure itself. We finally
discuss the origin of these systems, including their likely formation through
gas accretion and minor mergers, but conclude that major mergers are an
unlikely cause.
