The origin of Christmas gift giving is actually a relic of an old pagan custom called the winter solstice a holiday that was first celebrated in ancient Rome. People exchanged gifts during the holiday called Saturnalia. Saturnalia was a holiday observed between Dec. 17 to Dec. 23 and later extended to Dec. 25 (depending on which calendar you go by). This holiday was to honor the false god of Saturn, and was renowned and famous for wild parties, gift giving and sacrificing humans on Dec. 25 after subjecting them to cruel tortures and forcing them to do illicit sex acts in the days leading up to their deaths when they were murdered as a sacrifice to the false god of Saturn.  The first recorded date of December 25th being celebrated as Christmas was in 336 during the time of Roman Emperor Constantine's reign (the first Christian Roman Emperor). Pope Julius I officially declared that December 25th would be the date that people would celebrate Jesus Christ's birth.

Gifts were Given After People Were Sacrificed At the Temple of Saturn

"The holiday Saturnalia was celebrated with a sacrifice at the Temple of Saturn, in the Roman Forum, and a public banquet, followed by private gift-giving, continual partying, and a carnival atmosphere that overturned Roman social norms: gambling was permitted, and masters provided table service for their slaves.The poet Catullus called it "the best of days". It was the Roman equivalent to the earlier Greek holiday of Kronia, which was celebrated during the Attic month of Hekatombaion in late midsummer (1).
No where in the bible is there an example of a birthday for Jesus or for any followers of Christ.  However, Gifts were brought to Christ by the Wise men because they knew He was a King, the Son of God and not as a birthday celebration. It was commonplace during this period, for gifts to be brought to newborn kings. Christmas is not mentioned or celebrated in the Holy Bible.
According to the Encyclopedia Britannica Blog,  Christmas was not celebrated by original Christians but was celebrated in the 3rd century as the Winter Solstice following a Roman festival called Saturnalia where people exchanged gifts. Christmas was also celebrated as a birthday for  a popular false god of light and loyalty called Mithra (2) ​
Can Christ Be Glorified Through A Holiday Steeped in Pagan Rituals?
David C. Pack states, "Why do people think that Christmas is wonderful? It certainly felt wonderful to me. I trusted what my parents told me. I had no reason to doubt them. They were merely teaching me what their parents had taught them. I never questioned the true origin of Christmas!
Every aspect of Christmas has pagan origins. There is no way that Christ could be glorified by pagan rituals even though man has attached His Holy name to this pagan holiday-it is still in fact based on pagan rituals. 
Most never reflect on why they believe what they believe or do what they do. We live in a world filled with customs, but few ever seek to understand their origin. We generally accept them without question. Most people basically do what everyone else does—because it is easy and natural!
Let’s carefully examine the roots of Christmas. Let’s look at why people follow the customs associated with it. Why is it kept on December 25th? Did the early New Testament Church keep it? This booklet is filled with facts from history that, when placed together, paint a complete picture. Let’s avoid all assumptions and only accept what can be proven!" 

Origin of Christmas Part 2

Origin of Christmas Part 4

References:
​1. Saturnalia. (2017). En.wikipedia.org. Retrieved 5 December 2017, from https://en.wikipedia.org/wiki/Saturnalia
2. ​"Search". 2017. Encyclopedia Britannica. Accessed December 5 2017. https://www.britannica.com/search?query=origin%20of%20Christmas.