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Sometimes when I put my iPhone to charge when its dead; it comes on automatically when it is charging, and sometimes I have to physically turned it on.
For example, last night I was on my iPhone, at it died. I plugged it in, then like 40 min after I went to check and I had to turn it back on and it was charged.
This doesn't happen all the time. Most times it comes back on automatically.
When it comes to physical problems you might have to go to an Apple Store. Be sure to book in advance to make your meeting as quick as possible!
In cases like this, it could be due to a hardware issue and you might be eligible for a free replacement if your device is defective.
"Important: If iPhone is very low on power, it may display an image of a nearly depleted battery, indicating that it needs to charge for up to ten minutes before you can use it. **If iPhone is extremely low on power, the display may be blank for up to two minutes before the low-battery image appears.**". – Joonas Sep 5 '17 at 9:26