We investigate the enhancement of yields of strange and multi-strange baryons in proton-proton (p+p), proton-lead (p+Pb), and lead-lead (Pb+Pb) collisions at the Large Hadron Collider (LHC) energies from a dynamical core-corona initialization model. We first generate partons just after the collisions by using event generators. These partons dynamically generate the quark gluon plasma (QGP) fluids through the source terms in hydrodynamic equations. According to a core-corona picture, this process tends to happen where the density of generated partons is high and their transverse momentum is low. Some partons do not fully participate in this process when they are in dilute regions or their transverse momentum is high and subsequently fragment into hadrons through string fragmentation. In this framework, the final hadrons come from either chemically equilibrated fluids as in the conventional hydrodynamic models or string fragmentation. We calculate the ratio of strange baryons to charged pions as a function of multiplicity and find it monotonically increases up to dNch/dη∼100 and then saturates above. This suggests the QGP fluids are \textit{partly} created and that their fraction increases with multiplicity in p+p and p+Pb collisions at the LHC energies.