Thermalization of a closed quantum system is a problem of immense interest. In this talk, we shall, however, focus on the early time dynamics of a closed quantum system evolving with the time independent final Hamiltonian following a quench. The purpose is to probe the emerging non-analyticities at different instants of time referred to as so called "dynamical quantum phase transitions (DQPTs)". These non-analyticties are manifested in the Loschmidt echo and can be connected to the the lines (or areas) of "Fisher zeros" in the complex time plane. Furthermore, these are reflected in a dynamical topological order parameter constructed out of the gauge-independent Pancharatnam phase implying an emerging topological structure. With a brief note on the one-dimensional models, we shall illustrate the above scenario using the topological Haldane model on a hexagonal lattice. We shall illustrate the non-trivial role played by the Haldane mass term (which determines the topology of the equilibrium Haldane model) and also propose the topological index associated with the corresponding DQPTs.