This work studies the dynamic response of solar wind charge exchange (SWCX) soft X-ray emission in the Earth's magnetosphere to the solar wind proton flux. Unlike previous studies that attempted to use complex magnetohydrodynamic models to match the details of observed SWCX of a necessarily limited number of cases, this work focuses on determining the changes over individual observations in a much larger sample. To provide the cleanest test, we selected XMM-Newton observations when the solar wind proton flux changed suddenly by a factor greater than 1.5 and calculated the correlation coefficient between the SWCX emission in the 0.5-0.7 keV band and the proton flux. We find that the dynamical response is weak when the solar wind proton flux is low (<10,000 n * km/cc/s) because its variation is smaller than the uncertainty due to other emission components, but this response increases with the proton flux and its change value. The response is improved when the valence state of solar wind ions is high, as a higher abundance of ions generating SWCX can produce a greater correlation even though the proton flux is relatively low. It is conducive to the study of interplanetary coronal mass ejections (ICMEs) because ions in ICMEs are usually highly ionized. For XMM-Newton, the 0.5-0.7 keV band shows the strongest correlation, as the instrumental response decreases at lower energies and the SWCX emission decreases at higher energies. Moreover, the closer the satellite line of sight is to the subsolar magnetopause with the strongest SWCX emissivity, the better the correlation. Unified Astronomy Thesaurus concepts: X-ray astronomy (1810); Diffuse x-ray background (384); Solar coronal mass ejections (310); Solar wind (1534); Solar-terrestrial interactions (1473)