I received my 100% amethyst mat and have been using it for a few days now. It is extremely stiff and uncomfortable. Will this soften up and get more comfortable within the next few weeks?

It will soften up to some degree.

For thermal insulation and upward heat reflection, one of the bottom layers is made of thick compressed fabric and is really stiff in the beginning. It should become softer with time, but, of course, it will never be as flexible as bendable thin mats and pads.