How long did Adolf Hitler serve on the front lines as an infantryman in WWI before becoming a courier?

Q: How long did Hitler serve on the front lines as an infantryman prior to becoming a regimental message-runner?

If that question is meant to mean 'how long was the timespan between arriving in the combat zone at the front and being assigned as message runner', then the answer is 11 days.

Neither does that mean 11 days of continuous fighting nor that after that he was always 'safe' by virtue of some more physical distance between him and no-man's land. Artillery is often said to be somewhat of a dangerous nuisance.

On October 29th, 1914, at 0600, the man really arrived at the front during the Battle of Ypres:

Fridolin Solleder, who fought in 12th Company, later recalled that his company leader sent them off into battle with the words: ‘Men, we must attack! Conduct yourselves bravely! Good luck!’ The objective for the List Regiment was first to get past the hill, then to face the enemy in the hollow beyond, and finally to fight their way up the next hill. The primary goal was to throw the British out of the Flemish village of Gheluvelt on top of the hill and to break through towards Ypres.

which lastet 4 days, which the British regiments recorded as 'three great days' of which not all soldiers were equally deployed:

While their comrades from 3rd Battalion were fighting from house to house, Hitler and the men of 1st Battalion spent the attack on Gheluvelt inside the relative safety of a former British trench outside of the park of Gheluvelt Castle. […]

Nearly a quarter of all German losses in 1914 occurred at 1st Ypres. On the first day alone 349 men of the List Regiment died but the remaining days of 1st Ypres were no less bloody. By 24 November, the end of 1st Ypres, as many as 725 men of the regiment—or approximately one in four men—had died. Hitler, though, was still alive. Hitler’s survival was in part due to his assignment to 1st Company. Had he joined any of the companies of 3rd Battalion, he would have been twice as likely to die during the first seven days of combat. Had he been put with Ludwig Klein in 11th Company, the chances of him today being buried in some grave in Flanders and of a dramatically different twentieth century would have even been three times higher than the odds he faced through his service in 1st Company. The Highlanders of the Black Watch and the Coldstream servicemen had missed their golden opportunity to kill Hitler on the List Regiment’s first day of battle. […]

As Hitler celebrated Christmas, he was no longer a simple infantryman. His experience as a combat soldier and a regular infantryman had lasted only a few days longer than those who had died in the fields and hedges of Gheluvelt. Soon after the List Regiment’s initiation into the war, on 3 November (but retrospectively effective from 1 November), at a time when the List Regiment was desperately short of officers, NCOs, and troops of higher rank—when virtually all NCOs and higher-ranking NCOs had been promoted to fill the vacant ranks (as was Albert Weisgerber, who had become a Offiziersstellvertreter, or warrant officer)—Hitler had been promoted to Gefreiter. This was a promotion in the Bavarian Army still within the rank of Private in the US or British armed forces. It was a rank that did not provide Hitler with any power of command over other soldiers—as the rank of Corporal or Lance Corporal (which English-language publications tend incorrectly to apply to Hitler) would have done. […]

Another event which occurred around the same time transformed Private Hitler’s war to an even greater extent, an event without which Hitler’s life and that of the world he made would have been very different. Eleven days after arriving at the front, on 9 November, Hitler was made a dispatch runner and was assigned to regimental headquarters.
_{— Thomas Weber: "Hitler’s First War. Adolf Hitler, The Men Of The List Regiment, and the First World War", Oxford University Press: Oxford, New York, 2010. Page 53 in print, unpaginated on gBooks, [all emphasis above added, LLC]}