What was the first battle in history fought by vast-majority-% "distance-shooting" non-mechanized force?

I imagine the any action between Eurasian steppe tribes from the Mongols back to their ultimate forebears would qualify.

[The] question is:

What was the first battle that clearly was fought - by both sides - in the modern way, with vast majority of the fighting, by design, being done by firing projectile weapons at a distance?

"Modern" is one of these awful words that change their meaning with time. Longbows or catapults where once modern. But the question is more specific, and it requires that both sides in battle expected to inflict damage on the enemy by firing projectiles at a distance. And so, anything before the Napoleonic wars at very least is not the answer.

Historically, footsoldiers were divided into archers and infantry proper. Archers were used to "soften" the enemy, so that a direct assault by cavalry or infantry would be possible. These two different functions of footsoldiers could only be fused into one with the invention of the bayonnet. But this still doesn't answer the question: while a bayonnet equiped infantry would shoot as it charged, the final assault was still supposed to be decided by non-ranged edged weapons - the gun, with the bayonnet, used as a pike. A further change happened when armies started to expect shooting their enemies rather than stabbing them, even in the final assault.

While the fusion of infantry into one only force was quite sudden, with the bayonnet eliminating the need for separate bodies of skirmishers/chargers, this later change seems to have been much more gradual. The American Civil war battles, while probably dedided by gun power first and foremost, still featured violent final hand-to-hand clashes. The same is true for its South American equivalent, the Triple Alliance (or Paraguay) War. I am not sure of what proportion of casualties was exacted by bullets as opposed to those caused by blades (though I am sure both dwarfed in face of disenteria and other infectious diseases), but I very much doubt that the Union, Confederacy, Brazilian, or Paraguayan armies expected to damage their enemies mainly through bullets (as for the Argentinians and Uruguayans, I am pretty sure they expected the opposite).

In WWI, though, it seems clear that all armies involved - or at least the main ones - relied on machine guns as their main weapon to inflict damage. This is complicated, though, because the final assault - the conquest of a trenchline - still relied on bayonnet assault, resulting in an enourmous advantage of defences against attackers, with the known results - industrial scale senseless butchery, culminating in social unrest among the troops, with four empires being destroyed in the process by the combination of enemy onslaught and internal uprisings.

Such problems would only be solved by WWII style warfare - the use of armoured "cavalry", ie, tanks, plus tactical and then strategic use of air force.

So I would say, it was a long process, that started after the Napoleonic wars, and lasted up to WWII. At some point, there were more casualties caused by gunfire than otherwise; at a later point, military planners learned to expect this as the "normal" way of warfare.

Battle of Carrhae, 53 BC, between Roman general Crassus and Parthian Cavs. The Parthian army consisted of 9000 horse archers, and 1000 cataphracts. Note that the eastern cataphracts also carry projectiles. It is fair to say that ranged combat is one of their major doctrines. The Parthian did a failed charge, but then broke and routed the Roman legions mostly by distant shooting, 30-50 meters away.

Crassus' army pushed deep into the Parthian's desert area, lacking water and food. Upon learning about the presence of the Parthian army, estimated at around 10,000 cavs, Crassus's army experienced a sense of alarm and anxiety. Cassius, the top-ranking general under Crassus, initially recommended deploying the Roman forces in the traditional manner, with infantry forming the central formation and cavalry positioned on the flanks. Initially, Crassus agreed to this approach.

However, Crassus soon had a change of heart and ordered a different formation. He arranged his troops into a hollow square, with each side composed of twelve cohorts. This formation was designed to safeguard his army from being outmaneuvered by the Parthians, but it came at the cost of reduced maneuverability. As the Roman forces advanced, they reached a stream. Crassus's other generals advised him to establish a camp and postpone an attack until the following day, allowing his troops to rest. Nevertheless, Publius, one of Crassus's commanders, was eager to engage the Parthians immediately and successfully persuaded Crassus to confront the Parthians without delay.

Initially, the Parthian leader, Surena, had planned to break the Roman lines with a direct charge from his cataphracts, but he realized this wouldn't be enough. Instead, he used his horse archers to encircle the Roman formation. Crassus, the Roman leader, attempted to drive off the horse archers with skirmishers, but they were repelled by the Parthian arrows. The horse archers then engaged the Roman legionaries. Although the Romans were protected by large shields and armor, some of the arrows managed to penetrate the shields and cause injuries.

The Romans repeatedly advanced toward the Parthians in an attempt to engage in close combat, but the horse archers skillfully retreated and continued to fire at them. To protect themselves, the Roman legionaries formed the "testudo" formation by locking their shields together, making them nearly impervious to arrows. However, this formation limited their ability to fight effectively in hand-to-hand combat. Taking advantage of this weakness, the Parthian cataphracts charged the Roman line, causing panic and heavy casualties. When the Romans tried to break their formation to repel the cataphracts, the horse archers resumed their attacks.

Crassus hoped that the Romans could hold out until the Parthians ran out of arrows. However, Surena used camels to resupply his horse archers with more arrows. Realizing the dire situation, Crassus sent his son Publius with a contingent of troops to drive off the horse archers. The Parthian horse archers pretended to retreat, luring Publius' forces into an ambush. Publius and most of his men were killed, with only a few being captured alive.

The Parthian shootings continued until nightfall. Crassus ordered war cry and general advance, with little gain. After the sunset, the Parthian left contently. Covered by the dark, Crassus ordered a retreat to the nearby town of Carrhae, leaving behind 4,000 wounded soldiers who were subsequently killed by the Parthians the following morning. Finally, a few days later, the Romans were chased-up, and most of them killed or captured.

With more than 43000 well-trained soldiers, it is safe to say that if battle was mostly melee combats, Crassus would at least have a good chance.

Source: Plutarch. Life of Crassus

https://www.worldhistory.org/Parthian_Cataphract/

Because nobody said about naval battles, here's some nice (I hope) examples, sorry for citing Wikipedia only.

In 1178 BC or 1175 BC during the Battle of Delta distance attack was performed by Egyptian archers.

According to the Medinet Habu inscriprions, (...). Ramesses lined the shores of the Nile Delta with ranks of archers who were ready to release volleys of arrows into the enemy ships if they attempted to land. Knowing that he would be defeated in the battle at sea, Ramesses enticed the Sea Peoples and their ships into the mouth of the Nile, where he had assembled a fleet in ambush. This Egyptian fleet worked the Sea Peoples' boats towards shore. Then archers both on land and on the ships devastated the enemy.

I think that archers could have been placed on ships before this battle.

First use of artillery can be found in article about Greek fire:

Incendiary arrows and pots containing combustible substances were used as early as the 9th century BC by the Assyrians, and were extensively used in the Greco-Roman world as well.

The first naval use of cannons could be (from article about cannon):

The battle of Arnemuiden, fought on 23 September 1338, was the first naval battle using artillery, as the English ship Christofer had three cannon and one hand gun.

(The English eventually lost the battle).

During the Battle of Midway both fleets did not see each other. There were no shooting between them, only between planes and ships.

The first military submarine could be Turtle:

During the American Revolutionary War, Turtle (...) tried and failed to sink the British warship HMS Eagle, flagship of the blockaders in New York harbor on September 7, 1776.

This is not of course distance attack. The first one (or at least one of the most spectacular ever) could be German U-9's successful attack on three British warships on Sept. 22, 1914.

I would disagree with Tom Au's answer. The first examples of "modern warfare" engagements where both sides expected to prevail in battle with ranged weapons took place a few months into the US Civil War.

The key is the development of the rifle versus the musket. Prior to that, firearms didn't have an effective range sufficient to counter an infantry charge. The effective range of a rifle was just under 1,000 yards, so an advance of infrantry would need to "absorb" three or more volleys of accurate rifle fire before hitting the enemy line. The result was slaughter and stalemate.

The English did have a period where their longbow was a superior weapon that neutralized lesser-equipped archers and crossbowmen, but people fighting the English did not expect to win battles with missile weapons. In fact, the main objective of someone fighting the English was to avoid the bowmen!

One of the first and most obvious examples to me would be the Achaemenid Persian empire, their whole army composition was based on archery. They did use light spearmen, and the famous Anusya, but the first would only play a secondary role in the battle while the second was while an elite infantry unit also extremely skilled at archery. I can't seem to find an actual battle which is a good example. I found some information of Europa Barbarorum, a mod made by history enthusiasts.

The Achaemenid military organization was clearly made to facilitate archery, where a satâbam, or one hundred men, would mainly consist of archers who from the second rank (As the first rank consisted of spearmen who formed a defensive wall with the spârâ which in turn a decorated pavise of wicker) would continuously increment the angle, to the tenth rank. This would require a great discipline and a good number of junior officers, also ranked accordingly in a decimal manner to coordinate the formation properly. The wicker shields would be vital in outlasting the enemies in volley exchanges, but individual additions of armour facilitated this effect as well.

so 9/10 of the main infantry would be archers. Also while they did have a lot of cavalry these would have been primarily light skirmishing cavalry, that only occasionally engaged in hand to hand.

EDIT

I change my answer to the The Persian invasion of Scythia, not a single battle but an extended campaign. It was undertaken by Darius I of Persia early in his reign.*

As I explained above the Persian army was very much based on archery, They did still make use of light infantry, light cavalry and some heavy cavalry. The Scythian though only use of horse archery during this campaign.

Darius invaded Scythia, where the Scythians evaded Darius's army, using feints and retreating technique eastward while wasting the countryside, by blocking wells, intercepting convoys, destroying pastures and continuous skirmishes against Darius's army

So both armies had to rely on archery, the Scythians because they wanted to and the Persians because it was the only way to respond. Most casualties will therefore have been soht with bows.

• I can't find an actual date, but Darius undertook the campaign quite early in his reign (he reigned from 522 to 486 BCE)