How could Saint Luke have known about those stories of Jesus' early life in his writings?

Luke was a physician who had an inquiring mind. Besides traveling with the Apostle Paul and learning from him, Luke probably interviewed other Apostles and may have talked with Mary the mother of Jesus to compile his eyewitness accounts.

Luke 1:1 Many have undertaken to draw up an account of the things that have been fulfilled among us, 2 just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. 3 Therefore, since I myself have carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, most excellent Theophilus, 4 so that you may know the certainty of the things you have been taught.

Colossians 4:14 Luke the beloved physician and Demas greet you.

Apostolic instruction:

Luk 1:1 ¶ Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,

Luk 1:2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;

Luk 1:3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,

Luk 1:4 That thou mightest know the certainty of those things, wherein thou hast been instructed.

Just as anyone does who sets out to write a biography - biographers talk to people who knew the person in question.

maybe he made them up.