What is the first Christian Holiday in a year?

In the (Western) calendar year, that would be Epiphany.

In Western Christianity, the feast commemorates principally (but not solely) the visit of the Magi to the Christ Child, and thus Jesus Christ's physical manifestation to the Gentiles. It is sometimes called Three Kings' Day, and in some traditions celebrated as Little Christmas. Moreover, the feast of the Epiphany, in some denominations, also initiates the liturgical season of Epiphanytide.

https://en.wikipedia.org/wiki/Epiphany_(holiday)

It depends on how you use "year" and "holiday" in this context and also on the specific Christian denomination.

For the calendar year, it would be Epiphany as indicated by akg1486.

If you go by liturgical year (church year) and the ranking of feasts, however, it would be either Christmas Day or Immaculate Conception (not every denomination has that as a feast day). The liturgical year starts on the first Sunday in Advent.

Immaculate Conception is celebrated December 8 by those churches who have feast days related to the Virgin Mary. It is considered a solemnity (highest rank of feast days - the term "holiday" is not used) in the Roman Catholic Church.

Denominations who do not celebrate Marian feast days would encounter Christmas first.

https://en.wikipedia.org/wiki/Liturgical_year
https://en.wikipedia.org/wiki/Feast_of_the_Immaculate_Conception

I guess one needs to know what is meant by "Year", is it Calendar or Liturgical ? Liturgically, the year begins with Advent (Nov 30th) Advent ends with Christmas (Dec 24th). Christmas ends with the Epiphany (Jan 6th). After Christmas is "Ordinary Times" until you get to Lent / Holy Week, Lent begins with Ash Wednesday (This occurs on a different day each Calendar year, it is 40 day prior to Easter not including Sundays). After Lent / Holy Week comes Easter and after Easter it's Ordinary times until Advent.

https://www.bbc.co.uk/bitesize/guides/zqttdxs/revision/1

https://www.christianity.com/church/church-life/what-is-ash-wednesday-why-do-christians-celebrate-it.html

If it is the calendar year referred to here, 1 January itself is a Christian feast day, which varies with denominations. I got censored here yesterday when I submitted their actual names, which may have been seen as too close to 'bad' language. One is for a life event for Jesus, another is for his mother Mary, and there are also Saints Adalard of Corbie, Basil the Great, Joseph Mary Tomasi, Zygmunt Gorazdowski, Telemachus, and many others. See https://www.ulc.org/ulc-blog/christian-feast-days-celebrated-on-january-first, https://catholicreadings.org/saint-of-the-day-for-january-1/, https://en.wikipedia.org/wiki/Feast_of_the_Holy_Name_of_Jesus