Question: John 1:29 KJV

The next day John seeth Jesus coming unto him, and saith, Behold the Lamb of God, which taketh away the sin of the world.

John 12:47 KJV

And if any man hear my words, and believe not, I judge him not: for I came not to judge the world, but to save the world.

Answer: 
That the Father sent the Son to be the saviour of the world and that John declares of him ‘Behold the Lamb of God which taketh away the sin of the world’, does not suggest, in any way, a ‘Christian Universalism’, that is to say the notion that, automatically, all humankind shall be saved irrespective of their behaviour, irrespective of faith or irrespective of the purposes of God in salvation.

In order that there should be a world to come, at all, necessitated the coming of Christ and the death of Christ. It is clear from what the scriptures teach regarding restoration (unhelpfully translated ‘reconciliation’) that salvation is effected by the death of Christ and by union with Him, under his Headship, in a righteous restoration out from under the headship of Adam and out of the former human state in Adam.

Part of this restoration is the fact that Jesus Christ is the Lamb of God who taketh away the ‘sin of the world’ which does not refer to the specific actions of individuals (which is dealt with in other parts of the doctrine of Christ) but refers to the entry of sin into the world from the beginning, in Adam.

Being ‘made’ sin, or being effected sin (some translate this as ‘being made a sin offering’ but I suggest that that falls short of the full concept) sin, itself, was condemned within the humanity of Jesus Christ - a clean humanity - and sin was eradicated in the sight of God, righteously.

No individual is condemned, personally, for the liability of flesh and blood, or for the propensities of created humanity, or for the failure of man in the flesh, or for the transgression of the head of humanity, Adam. This liability and this sin is taken away by the Saviour and borne by him in his death.

That removal, righteously, is necessary for there to be a world at all. That removal was necessary even to grant a continuance to humanity after the Flood. The judgment on the world, by water, was to end all flesh because of the consequences of sin and because of the multiplication of evil on earth to the extent it could not be tolerated any further.

Eight persons were preserved and that preservation was in order for the purposes of God to be fulfilled, despite the transgression : a continuance being granted, due to a foreseen sacrifice (by Christ) that gave a righteous basis for the extension of the world, in time, for those divine purposes to progress.

Else, in righteousness, there could be no world at all. The world would have ended at the time of the Flood.

He is the ‘Saviour of the world’ in that humanity is granted existence, time, forbearance and the testimony of the gospel (whether by figure and ritual under the old covenant, or whether by full revelation under the New Testament) that they might be saved.

But if there is unbelief and rejection then that is the responsibility of each individual. And the consequence is to their own account, personally.

The further notion that the sufferings of Christ (within his body, prior to his death) were effective for the sins of all humankind (but only if certain individuals took advantage and added their own effectiveness) is nowhere expressed in scripture and is, in effect, salvation by works.
The question is a bit ambiguous, for it gives two quotes - John 1:29 an John 12:47 - which have quite different connotations: the first clearly shows that according to John Jesus' ministry is for the entire world and not just for one chosen nation of Jews, and there are quite a few passages in John that confirm the same. Thus, if in "universalism" is meant this, then of course, quite unambiguously, John's Gospel speaks about it.

However, the second quotation speaks about semantics of divine judgment and gives to this term a new twist, for we learn that Jesus who is God and equal to Father does not judge and neither does Father (John 5:22), but how then is God still the Judge who will judge all mankind? When names are applied to God, they change meaning drastically, and thus, we learn that God-the Judge does not judge - and if does not judge, then also does not condemn, for condemning is just a portion of judgment, which is a more general category - in the sense that He only forgives, He only loves, He only forbears, infinitely so, for He cannot help loving His creatures created in His image and likeness. Yet, when we reject all those divine actions towards us, close our hearts from them, then we condemn ourselves through the breach of communion with God and in a vulgar non-theological way this is called "God's condemnation", but, if one understands this vulgarly and in terms of positive human law-enforcement, one will obtain a sacrilegious calumny on all-merciful God, who in His own words "does judge nobody".

Thus, if in "universalism" is meant whether God saves all humans, then the answer is YES, He indeed saves all humans and cannot help saving them according to His nature, which can be defined as "love" (1 John 4:8), however, as being created free, we can reject His love and exactly through this free rejection self-inflict the condemnation on ourselves, His infinite forgiveness notwithstanding; for such real and horrible our freedom and responsibility is.