I always heard the 30-06 was our military's copy of the 8mm Mauser, any truth to it?
It's complicated. We had all kinds of influences and biases and prejudices.
The fact that we picked .30 (.308) has something to do with the .30-40 Krag being a predecessor. We had all the tooling to make .308 bullets. The fact that we were thinking Mauser-style and Mauser rounds has something to do with the 7X57 Mausers the Spanish were shooting at us in Cuba. The Mauser action was licensed from the Germans for our Springfield.
Once you've picked a Mauser-style action, the back half of the round pretty well dictates itself. The front half all has to do with the range at which you want to be effective. The middle has all to do with the propellent you can stuff behind the bullet. Somewhere in there, you have to figure out how much recoil the soldier can take and how much weight (rifle and rounds) he can effectively schlepp all day.
The Germans took all those factors and came up with 8X57. Remember: they licensed the action, they didn't give us the recipe for the powder. We took the parameters we had at the time and cranked the number and came up with 7.62X63. If you look at the evolution from .30-03 to .308 WIN over a half-century the propellents we used became more and more efficient. The nitro-cellulose we were burning in the 03 eventually gave way to the IMR powders Dupont developed during and after WWI. The "I" in IMR stands for Improved as in "Improved Military Rifle" This begs the question: Improved from what? The answer is the powder we were using when we adopted the .30-03 and 30-06. The '63' in 7.62X63 comes from how much of the old powder we needed to burn to get the .30 cal bullet to move the way we wanted.
Just an thought: the 7mmX57 is very close to the 7mm-08 in performance. The 7mm-08 is based on the .308 WIN which is a shortened 30-06. However, the US did not have powder for it in 1900, so we might have mixed things up differently and fielded something closer to the 280 Remington in WWI, or even (gulp) a .277 caliber. I'm sure the guys at the Springfield Armory would have staunched the idea-- they realized that the resulting buggery in the ranks would have depleted the Army's ability to fight.
