A novel numerical method is introduced for minimising the presence of scattering echoes in the frontal area of a dielectric ellipsoid through the application of the method of auxiliary sources (MAS) method. This approach utilises a Gaussian radio pulse that spans the frequency spectrum from 0 to 6 GHz. The approach involves determining the properties of an ellipsoid, such as its dimensions and a dielectric permittivity, using a specially developed MATLAB software package to make this ellipsoid invisible. This provides a valuable military and defence technology tool, particularly for stealth and invisibility technology applications. It is beneficial for avoiding detection by radar systems utilised for enemy surveillance and identifying concealed objects. This aims to eliminate the need for metamaterials for invisibility cloaking. The suggested methodology has been confirmed through a validation process, which involved a comparison of the outcomes derived from numerical experiments conducted during pulse echo observations using the FDTD method and an analytical solution. MAS offers a notable advantage over other methods and commercial software by significantly reducing computational time for simulating and analysing 3D dielectric objects. This allows for quicker consideration of various parameter scenarios and optimisation for desired outcomes.