Mormons believe in more than one god so how do they reconcile this belief with 1 Timothy 1:17?

First of all: I completely agree with all comments saying this question was already answered multiple times on this site.

However I would like to add an aspect here because it IS true that the Old Testament and the Book of Mormon stress that there is one God.

But context matters.

In these instances, including the part in Alma, the context and surrounding was such that it was necessary to stress there is only one God - the God of Abraham, Isaak, and Jakob. The context is other cultures believing in, or in Almas case, asking about, several Gods with each their own agenda(!).¹ Possibly even competing. If Amulek answers "no" then the answer will simply be "well too bad if your God won't save us, our God will save us though". If it's yes then... well then we get the answer we got namely "and you want to prescribe the one true God who to save?", more or less. There is no point in "yes, but aaaactually...". And there is of course always the option that the understanding of who is God was still incomplete. In fact, there is no point at which you could say that understanding is really, fully, complete.

See this quote from a seminary teacher manual from 2017, which the manual calls a "possible reason for Amulek’s answer that there is but one God":

“Is there more than one God? The question is often raised in response to Alma chapter 11, where Zeezrom, a critic, is contending with the missionary Amulek. …

“In order to understand Amulek’s statement [that there is but one true and living God], we must look at the full context. Throughout most of their history, many Israelites (forefathers of the Nephites) were eager to accept the numerous pagan gods of the Egyptians and Canaanites. Although the Book of Mormon is silent about the specific apostate notions held by the people in Zeezrom’s city of Ammonihah, it is clear that some apostate Nephites of Alma’s time were idolatrous—as some of their Israelite fathers had been. When Alma, Amulek’s missionary companion, was chief judge as well as high priest over the Church, he helped to establish a strong and faithful body of church members. Nevertheless, ‘those who did not belong to their church did indulge themselves in sorceries, and in idolatry.’ (Alma 1:32.) Apostasy was such a problem that Alma later gave up the judgment seat, ‘that he himself might go forth among his people, or among the people of Nephi, that he might preach the word of God unto them.’ (Alma 4:19.)

“As a missionary, Alma found that many of the people were steeped in idolatry. He discovered, for example, that the people in the city of Zoram ‘were perverting the ways of the Lord, and that Zoram, who was their leader, was leading the hearts of the people to bow down to dumb idols.’ (Alma 31:1.)

“This is the context, then, of the discussion Alma and Amulek had with Zeezrom. Seen in this light, Amulek’s answer is completely understandable and, of course, correct: There is only one ‘true and living God’—who shares none of his godhood with the hosts of false gods invented by man” (Roy W. Doxey, “I Have a Question,” Ensign, Aug. 1985, 11).

If today LDS taught in an environment of polytheism, they would also presumably focus on "one true and living God", as opposed to the idol gods of man.

Nicean teaching (forgive me if I butcher this) tries to reconcile the "one God" of the Old Testament and the three persons of the Godhead that are taught in the New Testament by saying that there are in fact three persons, but behind the scenes they are actually the same "essence" and that "essence", in full, is God. This teaching got defined in an environment where the false doctrines of the day were modalism, denying of Christ's divine nature, denying of Christ's human nature, and so on. If the false doctrines of the day were different, there is a good chance the creed could look quite different by stressing other points.

LDS are now in an environment where the Nicean teachings are the mainstream, so there is somewhat a focus on the distinctive teachings, which is that, yes there are three persons. Period. Christ has a fully divine, and a fully human nature, and so on. Basically most of what Nicea cared about, but no mystical "shared essence" to somehow save face regarding "monotheism". Simply three persons working as one. Not three Gods with different agendas like you would expect in polytheistic religions. Not three Gods that will answer your prayers differently. One God, three persons. The main reason why "Godhead" is used as term instead of "God" is because it would be confusing in a Nicean environment. The same goes for "personage". I am reasonably sure that word would just be "person" if not for the fact that word is already taken by Nicean doctrine, and reusing it would be confusing.

The problem with the Nicean creed is, among others, that it makes God an unknowable, mysterious entity, and by that reduces man to mere creatures, instead of literal children of God made in his image. We are told in the Bible that we should become perfect like He is, that we will be heirs together with Christ, but how is that believable if man is, even resurrected, fundamentally different from God.

Also, it's simply not how God chose to reveal himself to Joseph. So it was important to stress what was wrong in the minds of the contemporaries about who is God, just as in the time of the Nicean creed, the focus was on whatever the false doctrines of the day were (they did what they could, they just lacked the revelation necessary to get it right).

Towards polytheistic views, one God. Towards Nicean views, still one God(head) but three separate, individual, persons(personages), and nothing mysterious going on in the background.