Big Dreams in Chinese / Japanese...

遠大夢想 is a way to say “dream big” or “big dreams” in Mandarin Chinese.

大夢 means “Big Dream” in Chinese and Japanese.

大夢 is primarily a Buddhist term referring to the great dream that represents a long and winding life that feels like a dream (since reality is an illusion anyway in Buddhism).

This can also be a female given name, Hiromu, or Oomu, in Japanese. Also, more rare unisex given names Daimu or Taimu.

大望 is one of a few ways to write “dream big” in Japanese.

This is a good title if you want that to inspire ambition or high aspirations. 大望 is also a way to say “great expectations.”

鴻鵠之誌 is a Chinese proverb that implies that having grand ambitions also means that others will not understand your great expectations and ideas.

Though the actual words come from a longer saying of Confucius, which goes, “The little swallows living under the eaves wouldn't understand the lofty ambitions of a swan (who flies far and wide).”

This Confucius quote has led to this idiomatic expression in China that means “think big.” What you'd be saying is “The lofty ambitions of a swan.”

Note that Chinese people sometimes refer to the little swallow as one who does not “think big” but is, instead, stuck in a rut or just leading a mundane life. Therefore, it's a compliment to be called a swan but not a good thing to be called a swallow.

大志を抱 is a single Japanese word that kind of reads like a short proverb.

It suggests that you should have “high aims,” “ambitions,” or “aspirations” in your life.