I had good friend had a similar issue and these are all great ideas but it was not affordable for her to get a platform, storage bed, or even storage chests/boxes at the time. Do check the dollar store now for inexpensive under the bed chests/boxes. However, at the time all she could find to stuff under there, that were really cheap, were pillows to block it and they were literally a few bucks at the dollar store. It was soothing for her. Perhaps this would help instead if there aren't chests/boxes.

Congrats on getting the new bed. Excited for you! Nothing like a first purchase!