We show that the dynamics responsible for the variation of the Yukawa couplings of the Standard Model fermions generically leads to a very strong first-order electroweak phase transition, assuming that the Yukawa couplings are large and of order 1 before the electroweak phase transition and reach their present value afterwards. There are good motivations to consider that the flavour structure could emerge during electroweak symmetry breaking, for example if the Froggatt-Nielsen field dynamics were linked to the Higgs field. In this paper, we do not need to assume any particular theory of flavour and show in a model-independent way how the nature of the electroweak phase transition is completely changed when the Standard Model Yukawas vary at the same time as the Higgs is acquiring its vacuum expectation value. The thermal contribution of the fermions creates a barrier between the symmetric and broken phase minima of the effective potential, leading to a first-order phase transition. This offers new routes for generating the baryon asymmetry at the electroweak scale, strongly tied to flavour models. (C) 2018 The Authors. Published by Elsevier B.V.