Note: All my scriptural references are from the NKJV. The bold texts are the headings under which my path to an answer are carved.
a) The first Mountain in Daniel 2:44-45 represents God and his Kingdom
Deuteronomy 32:15 " But Jeshurun grew fat and kicked; You grew fat,
you grew thick, You are obese! Then he forsook God [who] made him, And
scornfully esteemed the Rock of his salvation.
Deuteronomy 32:18 Of the Rock [who] begot you, you are unmindful, And
have forgotten the God who fathered you.
Deuteronomy 32:19 " And when the LORD saw it, He spurned them,
Because of the provocation of His sons and His daughters.
Deuteronomy 32:30 How could one chase a thousand, And two put ten
thousand to flight, Unless their Rock had sold them, And the LORD had
Deuteronomy 32:31 For their rock is not like our Rock, Even our
enemies themselves being judges.
Mountains in scripture are symbolic of kingdoms. This is because the capital cities of almost all ancient kingdoms were founded on mountains.
Daniel 9:16 clearly illustrates this fact: “Let now Your anger and Your wrath turn away from Your city Jerusalem, Your holy mountain.” Throughout the Bible there are tons of examples in which mountains mean cities (Psalms 2:6; 48:1; Isaiah 66:20; Jeremiah 51:25; and Joel 3:17) e.g
Revelation 17:9 "Here is the mind which has wisdom: The seven heads
are seven mountains on which the woman sits. "There are also
seven kings. Five have fallen, one is, and the other has not yet
come. And when he comes, he must continue a short time.
b) How the symbol of mountains relate with Nebuchadnezzar's image
Mountains are composites of all that exists on earth. Iron, copper, gold, silver etc are dug out of mountains. Earth is a product of the decay of mountains. So the first mountain in this prophecy (Daniel 2:44-45) is the source or parent from which all the kingdoms in Nebuchadnezzar's image were born.
This is the Rock of ages and its king is the Ancient of days.
c) The Stone cut out of the mountain is a symbol of Christ according to OT and NT prophecy
The stone cut out of the mountain is the stone that will be used to build the mountain of the Lord's house.
Isaiah 2:2 Now it shall come to pass in the latter days that the
mountain of the LORD's house Shall be established on the top of the
mountains, And shall be exalted above the hills; And all nations shall
flow to it.
Ephesians 2:20-21 having been built on the foundation of the apostles
and prophets, Jesus Christ Himself being the chief cornerstone in whom
the whole building, being joined together, grows into a holy temple in
Matthew 21:42 Jesus said to them, "Have you never read in the
Scriptures: 'The stone which the builders rejected Has become the
chief cornerstone. This was the LORD's doing, And it is marvelous in
Isaiah 28:16 Therefore thus says the Lord GOD: "Behold, I lay in Zion
a stone for a foundation, A tried stone, a precious cornerstone, a
sure foundation; Whoever believes will not act hastily.
Zechariah 4:7 'Who are you, O great mountain? Before Zerubbabel you
shall become a plain! And he shall bring forth the capstone With
shouts of "Grace, grace to it!"
So the first mountain is the kingdom of God. The stone cut out of that mountain is Christ's earthly kingdom which will grow into a mountain; a final and an eternal world empire
Isaiah 9:7 Of the increase of His government and peace there will
be no end, Upon the throne of David and over His kingdom, To order it
and establish it with judgment and justice From that time forward,
even forever. The zeal of the LORD of hosts will perform this.