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 Hubble Space Telescope CANDELS imaging. We carry out a detailed analysis of this population, characterizing their number density evolution, masses, star formation rates and sizes. Overall, we find a surprisingly high overall number density of massive M* > 1010 M⊙ spiral-like galaxies (including clumpy spirals) at z > 1 of 0.18 per 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 ∼ (1 + z)−1.1. This is such that the absolute numbers of spirals increases by a factor of ∼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.