The increasing availability of information-rich data sets offers an invaluable opportunity to complement and improve the performance of existing model-based feedback algorithms. Following this principle, in this paper we present a novel class of Data-Enabled Extremum Seeking (DEES) algorithms for static maps, which make use of current and recorded data in order to solve a convex optimization problem characterized by a variational inequality. The optimization dynamics synergistically combine ideas from concurrent learning and classic neuroadaptive extremum seeking in order to dispense with the assumption of requiring a persistence of excitation condition in the closed-loop system. Using analytical tools for nonlinear systems we show that for a general class of optimization dynamics it is possible to tune the parameters of the controller to guarantee convergence in finite time to an arbitrarily small neighborhood of the set of optimizers. The results are illustrated in a scalar constrained minimization problem.