Childhood
You have 時代 as a "period" of time you're talking about. What period? The infancy years. Those years are not just when you're a baby, but when you were growing up, too. That was your childhood.
ようねんじだい
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
「昨日、幼年時代の友人に偶然会ったの。彼には何年も会っていなかったんだけど。」「そう言えば、サーモンって、幼年時代の友人のフグと結婚したのよね。」
"I ran into a childhood friend yesterday. I hadn’t seen him in years." "Speaking of which, Salmon married her childhood friend, Fugu."