Is a .375 H&H 300 grain solid tip enough for an Elephant?
Simple answer is yes.
But very important to brain it. When I hunted elephant my PH said a 375 is just fine.... but if you are off a bit on your shot, a larger caliber with give more shock and more likely stun the animal, knocking it down and giving you time for a follow up.
Of course the catch 22 is that almost every client is more likely to shoot a 375 more accurately than something larger
Another point, a smaller caliber tends to have better sectional density and penetrates better. A 375 loaded to specs with a 300 grain solid has really great penetration. And a 350 grain should be even better.
In my case the PH was very concerned about another bull very close to us potentially coming for us. So he was watching that animal rather than my quary. He had told me to shoot 3" behind the ear hole. I don't think he accounted for the perfect 90 degree angle the animal was at when i fired because the bullet hole was right there. The 416 Hydro solid missed the brain however it hit the neck vertebrae and knocked the animal down. I immediately put one between the shoulder blades and after getting closer (like 5 yards. It was down in thick grass and brush) a 3rd in the top of the head.
Another piece of advice. Unless you get the classic throwing the trunk up, back legs collapsing first brain shot... put another into the top of the head ASAP. Or get one through the chest vitals if you can't see the head. But put more lead into the animal before it has a chance to get up and run off. And if you don't drop it, try to hit the spine as it is leaving. But get lead into it!
My PH has a video where a client misses the brain but the animal drops. He turns around and wants to shake hands as the PH is literally begging him to shoot again. He is patting the top of head and pointing at the elephant. The elephant gets up and runs off as the PH is then shooting. He obviously did not want to shoot the clients elephant and there was plenty of time but the idiot client wasn't even looking. There is plenty of time for celebrating after all is secure. You also need to stay aware of your surroundings in case another elephant come charging in. It is Dangerous Game and they are killers!
It is an honor and privilege to hunt elephant! As well as potentially one of the best adventures you can experience. Enjoy