The Old Testament has many archaeological findings which confirm its existence many years ago. A good example would be the discovery of Dead Sea Scrolls with some of the scrolls estimated to be created around 300 years before Christ.
The New Testament also has many archaeological proof of existence. One good example would be Codex Sinaiticus estimated to be created about 350 years after Christ.
I have no idea about the archaeological evidence for the existence of Book of Mormon at least some 1000 years ago. Is there any discovery till date which suggests the existence of the Book of Mormon before Joseph Smith? Did any ancient scholar mention it? Was it ever quoted by ancient writers? Such an important book about Jesus Christ should leave some traces of its existence in the past.
(Please note that this question is not asking for the evidence of events in the Book of Mormon)