There is a shortcut worth knowing about for shallow damage, and a warning that comes with it: a thin coat of clear varnish or clear nail polish fills fine scratches optically and restores gloss without removing any material.
Thinning it slightly gives a smoother, less obviously coated finish. On a decorative item it can look very good.
The warning is that it is not reversible in any easy way, and for something with sentimental or collectable value that matters. Polishing removes material and leaves original surface; coating adds a layer that will yellow eventually and that a future restorer has to strip.
So for a toy you love, polish. For a toy you are patching up for a shelf, the coating is quick and effective.