The formal OBJ format specification does not include the opportunity to have per-vertex colour, only a per face colour through the MTL file standard. The usual approach of specifying vertex colour is to add the colour components, RGB as floating point values between 0 and 1, at the end of each vertex line.
So, if your file meets this format, you can try loading it into Character Creator and then go to the Scene Manager to switch the display option of the object to Smooth mode. This should allow you to see the colors.
If you don't see it, it's possible that the OBJ file was exported from ZBrush. Currently, OBJ files with vertex colors exported from ZBrush are saved in a different way that we do not support yet. We recommend exporting it as an FBX file format and using that instead.
Alternatively, you can use the GoZ feature, which supports importing vertex colors. For detailed instructions, please refer to the tutorial provided here.
https://courses.reallusion.com/home/character-creator/pipelines-and-render/zbrush-goz?v=utilize-zbrush-vertex-color-and-bake-textures-for-character-creator-%7C-pose-tools-and-post-link-tutorial