Recent results based on renormalization group approaches to Quantum Gravity suggest that the Newton’s and Cosmological constants should be treated as dynamical variables whose evolution depend on the characteristic energy scale of the system. An open question is how to embed this modified Einstein’s theory into Dirac’s theory of constrained systems. The Hamiltonian analysis for a renormalization-group (RG) scale dependent Newton’s and Cosmological constants action, Brans-Dicke like, is performed paying particular attention to Dirac’s constraint analysis. It is shown that the algebra of the Dirac’s constraints analysis does not close at the level of secondary constraints except in the particular case of an ADM metric in Gaussian normal coordinates. Brans-Dicke theory of Gravity is also studied as a Dirac’s constrained dynamical system since its similarity to RG-modified Einstein’s theory of gravity. The constraint algebra does not close at the secondary level as well as in the previous similar theory. Applications to the physics of the Early Universe is done in this setting. In particular, it is shown that in the Minisuperspace case with FLRW metric, RG improved Friedmann equations exhibit Bouncing and Emergent Universes solutions. While, in the classical case, Emergent universe solutions exist only for closed topologies (K=+1), in the sub-Planckian regime they hold also for flat (K=0) and open (K=-1) topologies.