No, it is not possible to remove a proton from a hydrogen atom without also removing the electron. In an atom, the proton(s) and electron(s) are bound together by electromagnetic forces. The number of protons determines the atomic number of an element, while the number of electrons determines its overall charge and chemical properties.
The hydrogen atom consists of a single proton and a single electron. If you were to remove the proton, the resulting particle would not be a hydrogen atom anymore, as the atomic number would change. It would become an ion, specifically a positively charged hydrogen ion (H+).
In nature, hydrogen ions are commonly found in ionized gases, plasmas, or in certain chemical reactions where the atom loses its electron to become a positive ion. Separating the proton from the electron requires a significant amount of energy, and under normal conditions, the electron and proton remain together to maintain stability.