"We develop a computationally efficient way of employing Gaussian wave packets to study laser-induced electron dynamics in atomic and molecular systems by directly solving the time-dependent Schr\"odinger equation (TDSE). First, we investigate charge migration (treating the nuclei classically), high-order harmonic generation (HHG), and single-isolated attosecond pulse generation in the Hydrogen molecular ion subjected to intense laser fields in a different range of frequencies with a basis of static coherent states (SCS). Then, seeking a smarter way of constructing and guiding a minimal set of time-dependent basis functions, we introduce a fast and accurate approach for optimizing s-type Gaussian type orbitals (GTOs) and apply it to calculate electronic states of different 1D and 3D time-independent systems. Finally, we apply our optimization approach to time-dependent problems. With our approach, we obtain excellent agreement with the exact results for HHG spectra of the 1D Hydrogen atom and molecular ion exposed to intense laser fields, which is not possible even with a much larger basis of static s-type GTOs. "