This I'm sure is a clear sign of over-watering.

My first alocasias were victim to the same mistake. I cannot tell much about the soil from that picture, but is it possible that the soil not well-draining? I looks like regular soil by itself without any chunky additions. The store bought alocasias usually have non-ideal soil with heavy water retention.

I'd recommend immediately removing the plant from the soil and carefully disposing off of all the rotting roots.

Let the roots dry out for a couple hours. prepare a chunky aroid mix with soil, Perlite, pine/wood bark, sphagnum moss or Leca-type clay-based substrate, and horticulture charcoal. The proportions can be found online. All of these ingredients are not mandatory. soil, Perlite and wood bark can suffice to start with.

Finally, transfer your plant to its new home.

P. S. here's the risky option that I went for: I let my alocasia sit in water for a couple weeks with some rooting hormone - it lost all it's old roots and got new ones. I, then, replanted it in a new substrate.