How was it possible for Jesus to be a sinless human being if we as humans are conceived in sin?

John Owen answers this question by pointing us back to the miraculous creation of the body of Christ by the immediate power of the Holy Ghost.

In other words, the virgin birth.

He writes,

“From this miraculous creation of the body of Christ by the immediate power of the Holy Ghost, it became a meet habitation for his holy soul. We have not only the general depravity of our nature, but the deviations of our own particular constitutions to conflict with. Hence, one is disposed to anger, another to levity, a third to sensuality, and another to sloth. But the body of Christ being perfectly pure and exact, there was no tendency in his constitution to the least deviation from perfect holiness. The exquisite harmony of his natural temperature, made love, meekness, gentleness, patience, benignity, and goodness natural to him, as having an incapacity of such motions as should have a contrary tendency. Hence, though he took on him those infirmities which belong to human nature, as such, and are inseparable from it till it be glorified, yet he took none of our particular infirmities, which cleave to our persons through the vice of our constitutions, or irregularities in the use of our bodies. Those natural passions of our minds, which are capable of being means of trouble, as grief and sorrow, he took upon him, and also those infirmities of nature which are trouble some to the body, as hunger, thirst, weariness and pain, (yea, the purity of his holy constitution made him more exquisitely sensible of these things, than any of the children of men;) but as to our bodily diseases and distempers which personally adhere to us, on the disorder of our constitutions, he was absolutely free from them. The human nature of Christ thus being miraculously formed, was sanctified from the instant of its conception, and filled with grace according to its capacity. Being not begotten by natural generation, it derived no taint of original sin from Adam; it was obnoxious to no charge of sin, but was absolutely innocent and spotless on the day he was created.”

John Owen