Manga about a boy who sacrifices himself to protect his parents from bandits, but is saved by a dragon

Pretty sure this is The Beginning After The End.

Plot points that match your description:

• The protagonist, a small boy named Arthur, is travelling to a town with his parents and some others, when their group attacked by bandits.
• Arthur and his mother have magical powers, but she can't use hers now because she's pregnant.
• During the struggle, Arthur is knocked off a cliff, but manages to take the last remaining bandit with him.
• Arthur wakes up at the bottom off the cliff, and discovers he's been saved by a mysterious being calling herself Sylvia.
• When he meets Sylvia in person, she initially appears as a giant humanoid clad in black armour. She later reveals her true form, that of a white dragon.
• Sylvia opens a portal to send Arthur back to his parents, at the cost of her own life. (She has a wound in her chest that gets worse the more she uses her powers.)
• As a parting gift, Sylvia infuses her unique 'will' onto Arthur, stating that his future development as a mage depends on how well he uses this gift.
• After going through the portal, Arthur finds himself in a forest, where he saves an elven princess named Tessia from a group of bandits.
• Arthur accompanies Tessia to her home, where he meets her family, including her grandfather, who decides to train him.