Which group of people was the first to willingly accept monotheism?

Answer 1

The oldest monotheistic religion still in existence today is Judaism, from Abraham onward. For Jews, that is a religious truth and is stated by Maimonides based on the Torah and tradition.
What about the Ancient Egyptians or Zoroastrians? In both cases, these were monolatrous henotheistic faiths. This means that they had multiple divinities with powers not completely constrained by other divinities.
Ancient Persia:
There is no consensus on when Zoroaster lived. Zoroastrianism is unlikely to be older than Judaism, and in addition Zoroastrianism is by most standards a duotheism.
ancient Egypt:
In the case of Atenism, although all of the heavenly gods were reduced to Amun-Re, the Pharaoh was himself still held to be a god.

Answer 2

1) According to careful research, the original tradition, which was widespread, was monotheistic. However, it died out completely in a relatively brief span of time. This belief does not refer to a specific people, country, or named religion, since it was not centralized or organized.

• Link: The original tradition
  

2a) The first continuous monotheistic tradition and religion as we know it, was and is Judaism, the tradition founded by Abraham. It began 3800 years ago, and its founding principle is that God is One. This was well before the Egyptian king Akhenaten, who in any case (according to tradition) was influenced by Israelite beliefs.

• Link: How Abraham founded Judaism
  

2b) Some might claim that monotheistic Judaism started later, as (for example) King Josiah made reforms in the late First Temple period. However, this is the view of secular academe, and flies in the face of tradition. Judaism had already been monotheistic for eight centuries by the time of Josiah. All he did was to eradicate the idolatrous influences of those Jews who had strayed from their own religion. This had happened repeatedly (such as with Jehoshaphat [2 Chronicles 17:6], and Samuel before him [1 Samuel 7:3-4]); and those who strayed into pagan practices never encompassed the entire people.

• Link: Were the Israelites monotheistic
  

3) Zoroastrianism, which might be suggested as another early contender, is not such a clear matter. There is no consensus on when Zoroaster lived. Moreover, the Zoroastrians believed in two gods, not one. The Jewish Sages who collated the Talmud in the early centuries of the Common Era lived in Babylonia, witnessed the practices of the Zoroastrians, and recorded this fact (Talmud, Sanhedrin 39a). In addition, in Zoroastrianism:

• there is worship through intermediaries, who are themselves "worthy of worship"
• evil and good each has its own creator
• some of its adherents believe in a self-creating universe
• some modern scholars see it as a form of pantheism.

See also the other Related Link.

Link: What do Jews believe about God?