We study the time variation of fundamental constants in the early Universe. Using data from primordial light nuclei abundances, cosmic microwave background, and the 2dFGRS power spectrum, we put constraints on the time variation of the fine structure constant α and the Higgs vacuum expectation value ⟨v⟩ without assuming any theoretical framework. A variation in ⟨v⟩ leads to a variation in the electron mass, among other effects. Along the same line, we study the variation of α and the electron mass me. In a purely phenomenological fashion, we derive a relationship between both variations.