Are there any conclusive facts to determine who were the first to believe in monotheism?
There are some elements of monotheism in the Rig Vedas:
Even the earlier Mandalas of Rig Veda (books 1 and 9), which contain hymns dedicated to devas, are thought to have a tendency toward monotheism. Often quoted isolated pada 1.164.46 of the Rig Veda states (trans. Griffith):
Indraṃ mitraṃ varuṇamaghnimāhuratho divyaḥ sa suparṇo gharutmān,
ekaṃ sad viprā bahudhā vadantyaghniṃ yamaṃ mātariśvānamāhuḥ
call him Indra, Mitra, Varuṇa, Agni, and he is heavenly nobly-winged
Garutmān. To what is One, sages give many a title they call it Agni,
Yama, Mātariśvan."(trans. Griffith)
One of the terms used to describe Hindu monotheism is Brahman.
The Rigveda is old:
It is one of the oldest extant texts in any Indo-European language. Philological and linguistic evidence indicate that the Rigveda was composed in the north-western region of the Indian subcontinent, roughly between 1700–1100 BC (the early Vedic period). There are strong linguistic and cultural similarities with the early Iranian Avesta, deriving from the Proto-Indo-Iranian times, often associated with the early Andronovo and Sintashta-Petrovka cultures of c. 2200 – 1600 BC.
I take this as evidence that people have been thinking and writing about monism, pantheism, monotheism, etc., since the dawn of recorded history.
Furthermore, the following quote describing the origins in Judaism describes Zoroastrianism as "dualist", in spite of the quote in the other answer which defines it as "monotheist".
Second Temple Judaism - Babylonian captivity
The Babylonian captivity had a number of consequences for Judaism and the Jewish culture, including changes to the Hebrew alphabet and changes in the fundamental practices and customs of the Jewish religion. Many[who?] suggest the people of Israel were henotheists during the First Temple period, believing each nation had its own god but that theirs was superior. Others suggest the people of Israel and Judah were polytheists, citing for example the presence of an asherah in the Temple. Some suggest that strict monotheism developed during the Babylonian Exile, perhaps in reaction to Zoroastrian dualism.
I take from that that there are different degrees/understandings/explanations of "monotheism", and therefore that "who were the first to believe in monotheism?" might be debatable or unclear. For example someone might say "Zoroastrians" or "Hindus" to which someone else might reply, "no that wasn't true monotheism".