We excavated about 30cm deep for our heat pump (6 people, filled ~2.5 tons), then backfilled with RC sand and compacted. On top of that, a 20cm concrete slab was formed and on top of that, 8cm XPS insulation boards were laid. However, it is also recessed in the elevated veranda and therefore needed a pedestal to reach the necessary height. In your case, you would just have to dig correspondingly deeper.
I actually have concerns that it might settle unevenly if you don’t excavate beforehand and create a stable base with gravel or something similar. On the other hand, with such a freestanding soft tub, you could also just play it "risky" and simply place a few XPS boards underneath; if it eventually settles, you just drain the water, move the heat pump to the side, and add material.