Are there any archaeological evidences suggesting the existence of the Book of Mormon?

There are several archaeological problems with the Book of Mormon. Several have suggested that items like parchment, scrolls and Codexes would not have survived, but as the book of Mormon mostly notes writings as being on metal plates, We would expect to see these writings. In Helaman 3:15 states:

But behold, there are many books and many records of every kind, and they have been kept chiefly by the Nephites.

(emphasis added)

Since metals are not subject to the same rot and degradation as parchment and scrolls, codexes made of metal would have survived. Were these writings truly as voluminous as described, we would expect to find them better preserved than stone tablets that are found in the Middle East. Were we to assume the writings not on metal plates unless otherwise specified, then the books and records kept by the Nephites are not truly of every kind.

Furthermore, the book of Mormon also lists several things like Barley, Elephants, Horses, Chariots, Iron and Steel as being common and present in large quantities, yet archaeologists do not find these kinds of items in North America dating to the times of the Book of Mormon.

You may find a good overview of these problems with Book of Mormon Archeology detailed here.

Finally, the Book of Mormon states that the Native Americans are descendant from Middle Easterners, but DNA samples of Native American remains do not agree with and confirm this ancestry for Native Americans.

These things tend to suggest that the Book of Mormon did not exist in any form prior to 1927 when Joseph smith recorded the Book of Mormon as we have it now.

We have a great deal of evidence for the histricity of the Book of Mormon but nothing comparable to what exists in support of the Bible. This is because archaeology in the Middle East is far in advance of archaeology in mesoamerica. The arid sands of the Middle East are an ideal environment for the preservation of artifacts. The humid Central American jungles are the worst place imaginable for that. We have contiguous occupation of the middle east preserving language including place names. We have at least four distinct waves of inhabitants in mesoamerica, each built on the ruins of the last and leaving us little trace of the original languages or place names. And we have a series of literate cultures in the Middle East, each preserving their language and writings in various ways compared to mesoamerica where we find very little evidence that any except the ruling class were at all literate. These area some of the challenges.

Here is some of what we have so far...
We have a great deal of evidence that falls into a single category of "got it right but couldn't have been known in 1830 by Joseph Smith."

1. Everybody knew (in 1830) that the Indian was a peaceful and pastoral people but the Book of Mormon describes great wars and strife among them.

2. The idea of sacred records preserved on gold was ridiculed since eveyone 'knew' that ancient writing were preserved on papyrus scrolls....until they began to uncover all sorts of metal leaf records from all corners of the globe during the 20th century.

3. The Book of Mormon spoke of cement being used which was impossible because they didn't have cement back then until cement buildings were uncovered at Teotihuacan.
4. The list of anachronisms that 'proved' that the Book of Mormon was a 19th century fabrication has been whittled down from 65 to 2. Barley, sheep, cattle, bees, swords, Kings, thrones, etc. all got crossed off the list.
5. The society and culture described in the Book of Mormon turns out to be spot on in a number of surprising ways when compared to what we now know of mesoamerica of 2500 years ago. For example, cutting off arms from ones enemies as trophies, fleeing to the top of sacred structures when threatened, erecting towers for public address.
6. The presence of Hebraisms in the Book of Mormon is remarkable and something impossible for Joseph Smith to have come up with (as they weren't known or understood in his day). Chiasmus is the most recognized and talked about but there are many more, like sentence structure that works poorly in English but well in ancient Hebrew, word choices that reflect a middle eastern understanding rather than an American (like saying "river of water" as though there were any other sort of river. In Arabia one would make a distinction between a river of water and a river that only runs intermittently but is currently dry, a river but not a 'river of water'). All of this is circumstantial evidence in support of the Book of Mormon being an actual historical document.

The only hard archaeological evidence of which I am aware is back in the Middle East (remember that the Book of Mormon is only mostly set in the new world. It begins in Jerusalem). The book describes Lehi's family traveling south southeast from Jerusalem for several days and then stopping to bury one of their number at a place called Nahom. In 1972 Carsten Niebuhr found, along the route described in the Book of Mormon, several day's journey south southeast of Jerusalem the city of NHM (Hebrew uses no vowels) identified by name engraved on the city gates.

Inventing an ancient city and then having an ancient city discovered that bore the same fictitious name would be an incredible stroke of luck. Inventing an ancient city and having it discovered where it was supposed to be and bearing the name it was given goes way beyond a lucky guess. Nahom is concrete proof (see what I did there?) of the historicity of the Book of Mormon.

To answer your question, I would challenge you to learn as much about the American continent as you can for the date that the Book of Mormon was compiled (~400AD). You will quickly discover that there are no other surviving records from that time period at all.¹ In fact, the oldest manuscript written in the Americas known by historians–the Dresden Codex–was written half a millennia after Mormon compiled the Book of Mormon, and is one of only 15 ancient Mesoamerican records left in existence.

The Spanish conquest of Mesoamerica erased most of the history there. Temples were torn down and Cathedrals were built upon their foundations. The vast majority of what we know about those cultures was written by their conquerers.

If there were any codecies that supported the existence of the Book of Mormon, they would have likely been destroyed around the same time all of the Christians in Mormon's time were slaughtered, or during one of Bishop Diego de Landa's purges, and had the Gold Plates or any other plates made of gold been discovered, they would have been melted down into ingots, just like Atahualpa's ransom, and sent back to Spain.

So no, there are no evidences comparable to the Dead Sea Scrolls, or Codex Sinaiticus that serve as evidence of the Book of Mormon's existence. It is unknown exactly how the scriptures were even shared with the people other than by the kings and prophets preaching to them. Mormon states in his book–The Words of Mormon–that the plate records he used to compile the Book of Mormon, which are briefly explained here, were handed down by the kings until they were delivered to him, who then spent a large portion of his life compiling them into the book which he delivered to his son Moroni, who finished the book, buried it, and 1400 years later revealed to Joseph Smith in resurrected form.

^{1 List of Existing Codecies of Mesoamerican Literature.}

Since there was only one set of plates, we could never expect to find direct archaeological evidence of them, as they are now in angelic custody. However, there ought to be indirect evidence that suggests their likely existence, and that is all this question can seek.

The Book of Mormon points to a highly literate culture that existed in the Americas for around one thousand years. During this time, they must have written numerous books on a great many religious and secular topics. Even if none of the books survived, we should find fragments of writing material and writing implements, as well as graffiti on rocks or walls. There is no archaeological evidence that points to the possible existence of the gold plates that Joseph Smith assures us he saw in 1830.

The Book of Mormon is said to have been written in a reformed Egyptian characters, but no archaeological, linguistic, or other evidence of the use of Egyptian writing in ancient America has been discovered. in 1966, John A. Wilson, professor of Egyptology at the University of Chicago, wrote:

From time to time there are allegations that picture writing has been found in America… In no case has a professional Egyptologist been able to recognize these characters as Egyptian hieroglyphs. From our standpoint there is no such language as 'reformed Egyptian'.

The "Anthon Transcript" (also known as the "Caractors" document) is a small piece of paper on which Joseph Smith, Jr. is said to have transcribed reformed Egyptian characters from the golden plates. This could be a more direct evidence for the existence of the plates, even if not strictly archaeological evidence. Klaus Baer, an Egyptologist at the University of Chicago, called the characters of the "Caractors" document nothing but "doodlings."