Just adding onto this. Someone else already talked about the hardware level, where the bits for a byte arrive simultaneously over a bus.

Generally this question is asked primarily by software people. It's worth noting that there's no way to access a bit in memory. The "atomic" level in modern computers is the byte. You can read a byte from memory, you can write a byte to memory. You cannot read or write a single bit.

That is to say that it doesn't matter what endian-ness the bit order is. There's no way for the CPU to ever peek inside the RAM to see how the bits are arranged in the byte. The memory could store it in completely random order, with each block of memory shuffling the bits differently from every other block -- as long as it send the data to the CPU in the expected fashion.