About what you're asking, a rumor of coming into Japan of Chinese boys and girls, it might happened around BC216, as story of 徐福 or 徐市.
司馬遷の史記の巻118「淮南衝山列伝」に、斉の方士（道教の徒で神仙の術を使う人・神仙の術なんてないので平たく言えば詐欺師です）徐福（徐市と伝える書もあります）が自分は不老長寿の薬を手にいれることができる、その薬は東方海上の三神山にあると秦の始皇帝に吹き込み、3000人の童男童女（この場合には若者という意味）と、百工（多様な職人）に、五穀の種と多数の船を用意させ東方海上に船出して、「平原広沢」の地を得て王となって戻らなかったとあります。
In the history book No.118 of 司馬遷's “淮南衝山列伝”, there's a referring of 徐福 or 徐市, as 方士 of 斉(方士 means a master of Tao, manipulating 神仙 magic, almost a fraud).
It tells that someday he brought some funny story into Emperor 始, that he was available of obtaining an immortal magic medicine, since he knew that the medicine existing on 三神山 mountain of far east.
Then he was granted 3000 of boys and girls(actually young men and women), many kinds of specialists, 5 sorts of grain seeds and lot of ships, by the Emperor.
Never came back since he went down forward the east sea, then they said that he might have been a King, found the place of “平原広沢”.
三神山とは、蓬莱、方丈、瀛州のことであるとされ、瀛州は後に日本を指す名称になりました。
三神山 means 蓬莱,方丈, and 瀛州, 瀛州 was later going to be a name pointing Japan.
The story of 史記, had been handed down into Japan too, then there's a lot of places which related to 徐福 coming.
Famous one would be 新宮 city in 和歌山 prefecture, there's a statue of 徐福 in 徐福 park, I had come and seen it once before.
There's another fake story around his trace, that 徐福 landed up 新宮, then traveled across a mountain till 大和, finally became Emperor 神武 himself.
余りにも古い話なので真偽のほどは全く不明ですが、中国文献に於ける倭の初出は「山海経」で、倭は帯方郡の東方海上にあり燕に属す、とありますから、燕が秦に滅ぼされる前に倭の存在は知られていたことになります。斉人の徐福は倭の存在を知っていて、中国の統一を果たすと同時に始まった、秦の圧政からの脱走を企てたのかも知れません。
It's not able to make sure of whether it was actually happened or not, first seen of 倭 in Chinese literature, is “山海経”, it says that 倭, placed at 帯方郡 of far east area, belonged to 燕, so 倭 would be already known before 燕 was destroyed by 秦.
Maybe, 徐福 had meant to escape from a cruel reigning of 秦, with his journey plan, which reigning was about to start enforcing as 秦's integration, since he somehow knew about 倭.
中国には、徐福が、始皇帝の焚書によって消滅した古典の書籍を倭に持って行ったという伝承があり、明代には日本に行けば焚書で消滅した古典が手に入るかも知れないと言われ、日本に行く商人に学者が徐福が持って行った古典探しを頼んだという話も聞いた事があります。
There was a rumor that 徐福, had taken out some Chinese books avoided the burning book of Emperor 始, so Chinese scholar men often asked merchants people, for looking for these ancient books, when they went to Japan for business.
「淮南子」という老荘の説に基づいて、治乱攻防、逸事、瑣談を記した書が史記の話の元ダネであり、東方海上の三神山も道教の神仙思想から来ているものと思われます。
There was a cited source of the 史記 story, as “淮南子”of 老荘.
Which was including the stories of 治乱攻防,逸事, and 瑣談, then the tale of far east area might have come from 神仙 principle of Tao.