The title says what I intend at the outset: to identify whether there is indeed scriptural basis for the teaching if Eternal Damnation or whether there is an alternative that suggests God will allow mankind to pay for their sins through suffering and then be accepted.
This argument is one of the apparent foundations of the Universalist Church and is creeping it's way into many theologies.
Matthew 25
46 “These will go away into eternal punishment, but the righteous into eternal life.”
Matthew 25
46 And these shall go away to punishment age-during, but the righteous to life age-during.’
Daniel 12
2 “Many of those who sleep in the dust of the ground will awake, these to everlasting life, but the others to disgrace and everlasting contempt.
Daniel 12
2 ‘And the multitude of those sleeping in the dust of the ground do awake, some to life age-during, and some to reproaches—to abhorrence age-during.
Acts 13
46Then Paul and Barnabas answered them boldly: “We had to speak the word of God to you first. Since you reject it and do not consider yourselves worthy of eternal life, we now turn to the Gentiles.”
1 John 5
11 And the testimony is this, that God has given us eternal life, and this life is in His Son.
12 He who has the Son has the life; he who does not have the Son of God does not have the life.
The Eternal life is what we get through obedience: but what of disobedience? Eternal life is eternal existence, so then not having His Eternal life will be an end, no? Once again, we must turn to the scriptures…
Psalm 90
1
Lord, You have been our dwelling place in all generations.
2
Before the mountains were born
Or You gave birth to the earth and the world,
Even from everlasting to everlasting, You are God.
Deuteronomy 33
27 A habitation [is] the eternal God, And beneath [are] arms age-during. And He casteth out from thy presence the enemy, and saith, ‘Destroy!’
”I will seek the *lost, bring back the scattered, bind up the broken and strengthen the sick; but the [Is 10:16] fat and the strong I will destroy. I will [Is 49:26] feed them with judgment.
(Whole Chapter: In context: )
Revelation 20
6 Blessed and holy is the one who has a part in the first resurrection; over these the second death has no power, but they will be priests of God and of Christ and will reign with Him for a thousand years.
14 Then death and Hades were thrown into the lake of fire. This is the second death, the lake of fire.
Revelation 21
8 "But for the cowardly and unbelieving and abominable and murderers and immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death."
Jude 1
7 as Sodom and Gomorrah, and the cities around them, in like manner to these, having given themselves to whoredom, and gone after other flesh, have been set before -- an example, of fire age-during, justice suffering.
Matthew 25
46 And these shall go away to punishment age-during, but the righteous to life age-during.'
Genesis 21
33 and [Abraham] planteth a tamarask in Beer-Sheba, and preacheth there in the name of Jehovah, God age-during;
This indicates that the translation to "eternal" may have been accurate as God is not God for just an age, unless the translators misplaced some commas:
Genesis 21
33 and [Abraham] planteth a tamarask in Beer-Sheba, and preacheth there, in the name of Jehovah God, age-during;
Deuteronomy 33
27 A habitation [is] the eternal God, And beneath [are] arms age-during. And He casteth out from thy presence the enemy, and saith, `Destroy!'
Deuteronomy 33
27
"The eternal God is a dwelling place,
And underneath are the everlasting arms;
And He drove out the enemy from before you,
And said, 'Destroy!'
Revelation 20:10 (American Standard Version)
10 And the devil that deceived them was cast into the lake of fire and brimstone, where are also the beast and the false prophet; and they shall be tormented day and night for ever and ever.
Eternal:
06924 qedem {keh'-dem} or qedmah {kayd'-maw} 


from 06923; TWOT - 1988a;
AV - east 32, old 17, eastward 11, ancient 6, east side 5, before 3,
east part 2, ancient time 2, aforetime 1, eternal 1, misc 7; 87
n m
1) east, antiquity, front, that which is before, aforetime
1a) front, from the front or east, in front, mount of the East
1b) ancient time, aforetime, ancient, from of old, earliest time
1c) anciently, of old (adverb)
1d) beginning
1e) east
adv
2) eastward, to or toward the East
Everlasting:
05769 `owlam {o-lawm'} or `olam {o-lawm'} 



from 05956; TWOT - 1631a; n m
AV - ever 272, everlasting 63, old 22, perpetual 22, evermore 15,
never 13, time 6, ancient 5, world 4, always 3, alway 2, long 2,
more 2, never + 0408 2, misc 6; 439
1) long duration, antiquity, futurity, for ever, ever, everlasting,
evermore, perpetual, old, ancient, world
1a) ancient time, long time (of past)
1b) (of future)
1b1) for ever, always
1b2) continuous existence, perpetual
1b3) everlasting, indefinite or unending future, eternity
No. God cannot be any more loving than to surrender His own Son to die that we may live. There will be no escape clause at the end, there will be no way out. Only through Jesus shall we find forgiveness. Reject Yeshua and you embrace eternal punishment.