Do we know if ancient stone sculptures/monuments from other cultures (e.g. Olmec, Egyptian, Buddhist) were painted similarly to Ancient Greek statutes that were made pastel colored and bright or was this a uniquely Greek style?

I can not answer for Olmec or Asian statuary, but ancient Egyptian art including reliefs, statuary and temple or monumental architecture was usually painted bright colours. These colours had important symbolic value in ancient Egypt as they represented or suggested themes like the sky or water (blue), growth or mummification (green), fertility or mummification (black), fire, masculinity or the desert (red), gold or femininity (yellow) and so on. In some cases these colours, or traces of them, have been preserved.

For instance, this statue of Akhenaten and Nefertiti still has its (now faded) paintjob which shows the beautiful details of clothing, jewellery and facial features.

Paintings from the ceiling of the Dendera Temple Complex are frankly stunning. Now that it has been cleaned a range of shockingly vibrant blues, reds, greens, whites and blacks are visible. The columns and walls of the temple were also painted.

You might like to take a look at the reading recommendations in the Art & Architecture section of the AskHistorians reading list on ancient Egypt. In particular, The Art of Ancient Egypt by Gay Robins will be a good fit for you as it has a lot of beautiful photographs.