Is the Hypostatic Union a contradiction?

It is possible for two statements to be true that are disparate. (But not contradictory.)

Light is known to have particulate form, for it is possible to send light, photon by photon, through a double slit and to see the individual photons register beyond the double slit in a pattern. But the pattern indicates that light is also a wave-form.

These would, at first glance, appear to be 'contradictory' and it it is only by further examination of the behaviour of light and the fact of quantum thermodynamics that we can understand that this disparate behaviour is not contradictory.

Similarly, what appears in scripture may seem (to our untutored mind) to be a 'contradiction'. Only with further understanding, and indeed with further spiritual revelation to faith, do we come to see the breadth and length and depth and height of the doctrine of Christ.

The scriptures declare that 'God was manifest in flesh', 1 Timothy 3:16 (TR/KJV) and that Mary 'brought forth the son of her, the prototokos' Matthew 1:25 (EGNT).

The scriptures also declare that the Son is 'come of woman', Galatians 4:4 (EGNT) and that God's Son, Jesus Christ our Lord, 'came of seed of David according to the flesh'.

Yet again, John tells us that 'the life, the eternal which was with the Father . . . was manifested' 1 John 1:2. And he also tells us that 'the Logos became flesh', John 1:14 (KJV).

It is very clear from these scriptures that two truths are being presented to us. They are not contradictory, though they are disparate.

The two truths do not merge, they do not mingle, they are separate truths.

The two meet only in the Person of Jesus Christ.

Only in His Person does Deity and humanity meet, without conflict, without disruption, without disorder and without contradiction.

Thus is he a mediator between God and humanity - 'humanity Christ Jesus, who gave himself' 1 Timothy 2:5 (EGNT).

In this matter I have had to be very specific about wording so I have quoted the literal translation of the Greek as given by the EGNT - the Englishman's Greek New Testament, which presents the Stephanus Text of 1550, and has an interlinear, literal translation.

Since you edited your question- changing "Christ is not God" to "Christ is human" - I have to express exasperation at such a rookie mistake. I will leave my initial answer but edit it myself to incorporate your change.

The proposition that "Christ is not God" is not one that is held by Christians who support the Trinity doctrine and who believe that the Logos incarnated as per John 1:1-14. Logos became flesh. Logos is a concept. It is an aspect of the Son. That aspect became flesh and was, thus manifest. So, 'God was manifest in flesh' for 'The Word became flesh.'

There are those who claim to be Christians but who deny the Trinity doctrine and who deny that "God was manifest in flesh" that "The Word became flesh".

The Christian claim that the Logos added human nature to his divine nature is in the ancient Nicene Creed. It states belief in one God the Father, maker of all things visible and invisible. It states belief in one Lord Jesus Christ - begotten, not made - true God of true God, of one substance with the Father, and through whom all things were made. This only-begotten Son of God "came down from the heavens, and was made flesh of the Holy Spirit and the Virgin Mary, and became man..."

The Christian faith does not teach that the Son of God "gave up" his deity in order to be man. That would render his sacrifice on the cross null and void. He had to be both God and man, though his glory was veiled while on earth. As this writer of the 18th century wrote:

"Nor did the incarnation of Christ bring a fourth person into the Trinity. The human nature of Christ is not a person; it is called a new thing, Jer. 31:33, and a holy thing, Luke 1:35 but not a person; for the human nature of Christ never had personal subsistence, or it never did personally exist alone or of itself, but it subsisted in union with the divine Person of the Son of God: "The Word was made flesh." John 1:14 (Divine Meditations, p55, William Huntington)

This is explained further in this article:

"Were not that unrevealed deity true of him in his humiliation on earth, redemption would have been impossible. Redemption necessitated that the Redeemer must be divine. Salvation absolutely required deity of this Saviour...

For it was the worth of his deity that gave an incalculably multiplied value to his manhood. His impeccable humanity gave him the absolute right to stand as the perfect substitute for the sinner. Man for man. But his divine nature and person enhanced that humanity and gave a value to his manhood beyond all calculation, extending the virtue of that substitution to a great multitude which no man can number [Revelation 7:9-10].

In the offering up of his spotless humanity at Golgotha, as the substitute of sinful men, that manhood of his was as it were cradled within the arms of his deity. Just as the shittim wood of the Ark was cradled in the gold with which it was overlaid.

In the incarnation the Son of God united with his divine nature that impeccable human nature created within the womb of the virgin Mary; and at the cross he offered up that humanity a spotless sacrifice to God om behalf of all those who he came to redeem. ... Thus his sacrifice became of sufficient substitutionary worth for so great a multitude, because his humanity was as it were offered upon the altar of his deity...

Thus he is Jacob's ladder in his nature and in his sacrifice; he reaches up to Almighty God and reaches down to the Israel of God. He is the one mediator, but one between God and men, because he unites both natures in his one singular person, and reconciles each in his unique sacrifice." (The Son of God, Romans 1:1-4 article by John Metcalfe, "The Ministry" magazine, Vol. 35 No. 1)

Thus there is no contradiction in the Trinity doctrine. Both natures were, together, manifest in the Saviour, the one Mediator between God and men - 1 Timothy 2:5 & Hebrews 9:15 & 26-27. The Bible is your best source for grasping this deep doctrine, for the Holy Spirit inspired its writing and will guide the understanding of those who approach in true humility and faith.

Is it contradictory to claim that Christ was both fully man and fully God at the same time?

No, because Jesus being God could operate under both natures at the same time.

The easiest way to understand how it works is to conceive Jesus (as God) from eternity "joined" humanity (incarnated as a baby; incarnated means "taking on flesh") by "putting on" / "adding on" human nature while remaining divine, thus adding a self-imposed "restriction", similar to an actor putting on very dark contact lenses to act as a blind person in a movie. This actor still has perfect vision, and can at times remove his contact lens to see perfectly.

For a short 11 minute video that explains this, please watch Eleonore Stump explaining Jesus as God according to the Chalcedonian definition (one person, two natures):

... for our salvation (born) of Mary the Virgin Theotokos as to the Manhood; One and the Same Christ, Son, Lord, Only-begotten; acknowledged in Two Natures unconfusedly, unchangeably, indivisibly, inseparably; the difference of the Natures being in no way removed because of the Union, but rather the properties of each Nature being preserved, and (both) concurring into One Person and One Hypostasis; not as though He was parted or divided into Two Persons, but One and the Self-same Son and Only-begotten God, Word, Lord, Jesus Christ; ...