Dylan,
They will usually sprout out fairly quickly when damaged as you described. So long as the trunk part is rooted and getting watered adequately, the only other factor may be nutrient levels. Sometimes an Alocasia will not come up because it does not sense adequate nutrients available. The other factor is whether the soil temps are warm enough.
Another idea is to dig it out, inspect the part below ground for roots and possible below-ground sprouts, and then replant in well-draining soil mix with timed-release fertilizer added.
Any other information (such as, is the plant in a pot or in the ground) you can provide may help me offer better advice.
Kind regards,
LariAnn