Absorb Elements says:
Casting Time: 1 reaction, which you take when you take acid, cold, fire, lightning, or thunder damage
Duration: 1 round
The spell captures some of the incoming energy, lessening its effect on you and storing it for your next melee attack. You have resistance to the triggering damage type until the start of your next turn. Also, the fist time you hit with a melee attack on your next turn, the target takes an extra 1d6 damage of the triggering type, and the spell ends.
This seems to imply that the caster avoids some of the incoming damage, but it isn't stated as explicitly as similar abilities of other spells, such as the Shield spell which states (in part):
Until the start of your next turn, you have a +5 bonus to AC, including against the triggering attack
Are others reading the Absorb Elements spell as I am, as similarly granting the resistance beginning with the triggering attack?