The paper introduces an improved Hamiltonian constraint operator in loop quantum cosmology (LQC) for a spatially flat, isotropic model with a massless scalar field. This new operator retains the key features of the existing dynamics, such as the use of the scalar field as 'emergent time' and the replacement of the big bang by a quantum bounce, but addresses a significant limitation of the current framework. Specifically, the new constraint operator ensures that the quantum bounce occurs only at a Planck-scale density, regardless of the momentum of the scalar field. This modification is motivated by physical considerations and is implemented in a more satisfactory manner, making the quantum evolution free from the drawback of occurring at low matter densities. The paper also discusses the Wheeler-DeWitt (WDW) theory, which is obtained by ignoring quantum geometry effects, and constructs the physical Hilbert space, Dirac observables, and semi-classical states. Numerical evolution of these states backward in time shows that the big bang is replaced by a quantum bounce when the matter density reaches the Planck scale. The key innovation lies in the implementation of the physical idea of incorporating the area gap in the curvature operator, which leads to a more physically motivated and conceptually compelling Hamiltonian constraint.The paper introduces an improved Hamiltonian constraint operator in loop quantum cosmology (LQC) for a spatially flat, isotropic model with a massless scalar field. This new operator retains the key features of the existing dynamics, such as the use of the scalar field as 'emergent time' and the replacement of the big bang by a quantum bounce, but addresses a significant limitation of the current framework. Specifically, the new constraint operator ensures that the quantum bounce occurs only at a Planck-scale density, regardless of the momentum of the scalar field. This modification is motivated by physical considerations and is implemented in a more satisfactory manner, making the quantum evolution free from the drawback of occurring at low matter densities. The paper also discusses the Wheeler-DeWitt (WDW) theory, which is obtained by ignoring quantum geometry effects, and constructs the physical Hilbert space, Dirac observables, and semi-classical states. Numerical evolution of these states backward in time shows that the big bang is replaced by a quantum bounce when the matter density reaches the Planck scale. The key innovation lies in the implementation of the physical idea of incorporating the area gap in the curvature operator, which leads to a more physically motivated and conceptually compelling Hamiltonian constraint.