This is the 1608th most frequent Japanese word.
抱い
"抱い" is not a standalone word; it is part of conjugations of the verb "抱く," which means "to hold," "to embrace," or "to harbor."
In this sentence, the word '抱い' (da-i) is part of '抱いて' (da-i-te), derived from '抱く' (da-ku), which means 'to hold or embrace'. It demonstrates the physical act of holding something.
彼女は赤ちゃんを優しく抱いています。
She is gently holding the baby.
Here, '抱いて' (da-i-te) figuratively means 'to hold in one's heart or mind,' as from '抱く' (da-ku), signifying emotional or conceptual embrace.
夢を胸に抱いて進みましょう。
Let us move forward while holding dreams in our hearts.
In this context, '抱かせました' (da-ka-se-mashi-ta) refers to 'giving rise to or fostering' hope, using the causative form of '抱く' (da-ku).