my pygmy date palm trunk fell on the ground
I have had this palm tree for about 6 years. Even though it fell on the ground, it's still growing.
Certified GKH Gardening Expert
If it fell because of wet muddy soil and maybe a wind event, then it may still have enough roots in the soil to sustain growth. You can leave it as is and not try to right it; in time the new growth will turn up and resume the vertical growth habit, even though the lower trunk remains horizontal.
If the trunk fractured or completely uprooted and that happened recently, the palm may still be growing from stored water and nutrients and not from root uptake, and it won't last through the summer.
If you want to try to set it back up straight, it requires some judgement and special handling. If the soil is still muddy wet, or if you soak it, you may be able to straighten it up a bit until you encounter heavy resistance. Don't force it or you may break the roots that are still intact. Prop it up with triangular rigid support bracing from below. And/or install guy wires/cables to stakes in the ground or to other trees or a wall if available.
Another option and probably the most practical, is to dig it out with a good soil-root-ball and replant it in a straightened position. Consider hiring professional help with palm transplanting experience.