Crusader Kings III

Start as King Louis II of Italy in 867 (The Caroligans)
- There will be an ongoing war as you start, click on the war progress icon on bottom right and choose surrender or else you wont be able to start pilgrimage until war is over.
- Open Decisions, choose to go on a pilgrimage and select Jerusalem for extra piety.
- You will get pop-ups during this journey with choices to make, pick choices during this journey that will increase piety.
- Select the religion icon on bottom left of the screen and click on Pope Nicholas, use Gold to seek indulgences from the Pope when possible for piety (100 gold is required each time).
- When you have 2225 piety click on the religion symbol bottom left on screen and select create new faith. - Click on and change one of the main doctrines. You will also have to choose a faith icon, type a faith name, and fill out all of the corresponding boxes (followers, description, etc.) in order to be able to create a new faith. The name and icon as well as information put into these boxes doesn't matter, you just need to fill it out before you can create a new faith.

The Ásatrú faith gives Piety through human sacrifice. Prisoners of a foreign religion can be killed without penalty. You can get 100+ piety per sacrifice. Easiest way is by playing as Sweden. They start of strong and snowball easily.

Declare war against someone and chose "Raid for Captives against [country]"; The cost is negligible. You'll capture prisoners through sieges, so go for the biggest cities. Once you reach 100%, enforce your demands, and you'll get more prisoners as a reward. Usually around 5-6. Depends on country size. This will net you several thousands of Piety, and fast.

This can be fairly easily accomplished in most playthroughs, but to give yourself a good boost:

-In 867, start as either King Louis II "The Younger" of Italy
-In 1066, start as Amir al-Umara Abu-Bakr ibn Umar of the Almoravid Grand Emirate

There may be better starting rulers than these two, I'll update if I find better starting positions - note that this is much more difficult in certain religions where pilgrimages are not an option.

Whichever ruler you choose:
-For your Lifestyle, choose the Theology Focus under the Learning Lifestyles and add perks into the Theologian tree - specifically, you want the "Prophet" perk, but the "Theologian" trait for finishing the tree is also very useful for this achievement.
-Every 15 years (or when it becomes available), go on pilgrimages (in your Decisions menu) to Jerusalem or your religion's furthest holy site.
-In every decision, choose the option that grants Piety, if available. Refrain from spending Piety where possible.

Once you have 2200-2300 piety, you can open your Religion overview (bottom of your screen next to your character) and choose to create a new religion. Simply change one of the major tenets of your religion (the change cost for each tenet is shown, so pick a cheap one), give your religion some basic details (name, emblem, etc.) and create a new faith.

BONUS: Keeping it in the Family: If you want to double down on achievements in one playthrough, under Marriage Doctrines of the Create Faith menu, change the Consanguinity option to "Unrestricted Marriage" and the Marriage Type option to either "Polygamous" or "Consorts & Concubines" (your religion may already have one of these options!). Changing these doctrines will slightly increase the cost, but they do make getting this achievement easier, as it will allow you to take direct relatives as spouses and concubines, making it much easier to birth a child with the "Inbred" trait.