It wasn't a complete change on a global scale up untill WW1, instead there whas a slow shift towards this style of warfare.

During the mid 19th century, many major pitch battles started being fought around defensive positions, where one side would asault another side entrenched in a redout or fort next to a point of majour interest such as a road, a city or bridge, perhaps the first example of such a battle is the battle of Borodino where Napoleon asaulted a series of Russian redouts blocking his way to Moscow. During the following years, the dynamic of pitched battles shifted more and more towards Borodino, defensive battles started to change in purpose for the defenders. Traditionaly one would defend in a fortress in desperation against an enemy that outmatched him, now the defenders seeked defensive battles in order to grind down the enemy, when you are defending your home soil, you don't have to attack the enemy, he needs to attack you, so you can effectively turn a defensive battle into a grinder for the enemy army and even if you loose, if you have inflicted enough casualties on the enemy, it may still count as a win (this is what happened at Borodino where the French got in control of the redouts but the Russians inflicted such devastating casualties on the French that many consider Borodino a tactical Russian victory). Thus the dynamic had changed, instead of having two armies going at it, you would usualy have an attacker and an entrenched defender. As I said, many major battles in the second half of the 19th century and early 20th century would go like this, perhaps the first conflict which featured something remotely similar to a WW1 frontline is the American Civil War, while it did not feature a continuous line of trenches, large segments of both armies where concentrated around defensive positions, The Battle of Getysburg and The Siege of Petersburg ilustrate this dynamic well.

Other examples include but are not limited to:

The entire Ruso-Turkish War of 1877 where The Rusian and Romanian armies cleaned up the Ottoman redouts in Bulgaria (ex: Siege of Plevna), not a single Napoleonic line battle was fought during that war.

The Ruso Japanese war where pretty much every major battle folowed this dynamic, see The Battle of Mukden which was perhaps the most WW1 style of battle up untill that point, featuring 262 000 Japanese asaulting 340 000 rusians it was the largest battle in human history fought untill that point, the scale of the battle was unprecedented, in just 30 days(the duration of the battle), the Rusians and Japanese consumed more amunition than the French amd Prusians during the entire Franco-Prusian War.

This new style of defensive battles was also favoured by new technology, breech loading rifles could be quickly fired and reloaded while prone compared to muskets favouring a defensive position, howitzers and explosive shells made densely packed Napoleonic style infantry formations and open field combat suicidal and machineguns made gap closing tactics such as cavalry charges obsolete and bayonet charges extremely costly.

So there are two factors that eventualy led to the age of continuous front warfare, a new military doctrine regarding defensive battles and new technology.

With these factors in mind we can now point out the begining of continuous front warfare, 1914 WW1, while the first half of 1914 went similarly to conflicts previously ilustrated, the halt of the Russian advance in East Prusia at Tannenber in August and the halt of the German offensive in France at river Marne in September marked the begining of the stalemate on both fronts fronts. By late Autumn, the Eastern and Western Fronts had been stabilised and both sides where entrenched on fronts stretching thousands of kilometres.