In light of a claim made by the Book of Mormon, that ancient Jews from the Pre-Exile period of the history of Israel practiced baptism for the remission of sins - akin to early Christianity - I was wondering if there was any archaeological evidence to back this claim up.
Otherwise I am curious as to when the practice first began and what the archaeological record says about the practice and its development.
The Jews had (and still have) a concept of ritual impurity/uncleanliness. I've seen authors though who dislike those translations, as the concept of ritual impurity didn't mean that the person was in a state of sin, or that they were actually physically dirty. It just meant that they weren't eligible to perform certain holy duties. Sources of impurity included menstruation, ejaculation, childbirth, dead bodies (including many types of animal corpses and some insects bodies), and many forms of disease. Again it needs to be emphasized that this was simply a ritual impurity, not a sin. Caring for the sick, proper treatment of the dead, etc were all positive things within the religion.
Part of the process of returning to ritual purity required a ritual bath or immersion. This would be different from a regular bath where a dirty person would clean themselves. This ritual bath was simply a quick immersion for ritual reasons. This was regularly done in a pool called a mikveh. But for certain purposes was supposed to be done, in "living water," moving water connected to an original source such as a spring or artesian well. As such most, if not all, of the mikvehs were connected to such "living waters."
The ancient Israelites had a lot of these mikvehs for people to immerse themselves in to return to ritual purity. In particular there are several near and on the Temple Mount, where ritual purity was vital (being where many unique rituals were performed). Where it was possible and appropriate streams and rivers were also used, like the River Jordan. But this was not done for the remission of sins. Sins were cleansed through sacrifices (in particular the Chatat (sin offering) and Asham (guilt offering)). Sins could also be removed through prayer, fasting, and good works. At no point in the temple periods, or pre-temple periods do we hear of baptism or ritual bathing to remove sin. The first time we hear of it being used to cleans sin directly (as opposed as a preliminary step to prepare for a proper offering) is with John the Baptist and other 1st century Jewish charismatic communities. And of course it took off with Christianity.
So while a ritual bath/immersion/baptism was common in pre-Christian Jewish/Israelite communities, most Jews went through a ritual immersion several times a year, it didn't have the same purpose or import as a Christian baptism.
2 Kings 5:14 refers to Naaman "dipping" (tabal; baptism means being "dipped in") in water for ritual cleansing (resulting in healing from a skin disease as a sign from God to Naaman). See references at https://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=H2881&t=KJV, https://www.blueletterbible.org/search/dictionary/viewTopic.cfm?topic=VT0000215 .
Sorry this doesn't meet the requirements for a full answer but I figure it's excusable as it's a point of fact not yet mentioned.
Also this reference on Baptism in the Early Church may be of use, https://books.google.co.uk/books?id=xC9GAdUGX5sC&lpg=PA327&ots=BtdP3XKRvz&dq=2%20kings%205%3A14%20baptism&pg=PA327#v=onepage&q=2%20kings%205:14%20baptism&f=false.