Historically, armies usually had a balance between warriors with projectile weapons (bows/guns) and close combat edged weapons (sword/pike/axe etc...).
This was necessary because ranged weapons of the time were not good enough to prevent armored-enough (or just fast-enough) force to close in with the shooters and hack them down with swords.
In some armies the same warriors fulfilled both roles (e.g. Mongols, gun-equiped cavalrymen of 30 year war, or bayonetted riflemen), but the "swordsman/pikeman" role was just as required as with separated roles. Even Mongols, after raining down arrows on an enemy, closed in for edged weapon fight - same with 30-year-war cavalry or infantry tercios.
This is obviously not the case today, where handheld edged weapons are a last-resort backup and rarely used in full-on combat outside urban fighting, or even including it.
My 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?
To clarify the question in response to comments:
"At a distance"- Simply means that the casualty was inflicted by a solid object propelled away from the soldier, and NOT held in the hand. In other words, a bullet shot from a gun counts. Clubbing over the head with the gun stock doesn't.
"Vast majority"as measured by either:
Most importantly, casualty ratios from ranged weapon wounds vs. handheld weapon wounds.
Yeah, a US Army infantryman today is trained and able to kill an enemy with a bayonet, an entrenching tool, a combat knife, or a pencil or toothpick if need be. But in a random infantry-on-infantry battle, how many enemy casualties are inflicted by toothpicks, how many by bayonets/knives, and how many by bullets?
Alternately, by attempted attacks (where attempted attack is a fired bullet or a single strike with edged weapon)
"By design"- meaning that your doctrine, your training, and your expected and actual battle intends for that vast-majority fighting (as defined above) to be with ranged weapon.
This is important to eliminate useless trivial example where a small force came in for regular ancient-style sword infantry fight, got 10 people killed at a distance from a bow, got frightened and ran away before closing in because the enemy was too numerically superior. The casualty ratio is 10/0 for range weapons, but that is by accident, not design.
This is about personal ranged weapons (say, man-portable). Bows, rifles, muskets.
It excludes things like artillery/airplanes/tanks.
 - Minor complication would be included in whether hand-thrown edged weapons count as range weapons (which might plausibly introduce as a possible answer some Javelin-exclusive battle I'm not aware of), as hand-held edge weapons (in which case "range weapons distance" must be increased to exceed throw distance), or simply ignored which introduces neither of those 2 complexities