Learn English – Other ways to say ‘each other’

Just saying “between each letter” raises the question of between each letter and what other thing? Between always involves more than one thing.

What you mean here is clear enough to most readers, but perhaps it would be more felicitous to write “between each pair of letters” — or more simply, just “between letters”.

Either of those work to provide between with more than one argument. However, don’t worry about the arguments provided being exactly two; they don’t necessarily need to be. That’s a myth. It is a fallacy to assume that between has only two entities. It simply is not true.

Quoth the OED:

In all senses, between has been, from its earliest appearance, extended to more than two.

Only the case-of-one doesn’t make any sense:

1. *Between your mother, they’ll come up with something.
2. Between your mom and dad, they’ll come up with something.
3. Between the three of us, we’ll come up with something.

All the other cases — including all your nieces and nephews and cousins and aunts and uncles — are all of them just fine.

Here are a few idiomatic phrases that imply a quick start to a continued action in slightly different ways.

Jump-start ( this is about starting a car and perhaps more about "re-starting" so perhaps not perfect)

Leap into ( perhaps implies getting into an action already in a dynamic state)

Dive in ( perhaps more about 'immersion' and sink or swim than forward momentum, although "diving start" might be hit another)

"bootstrap" is a different concept of 'self starting' 'picking oneself up by one's own bootstaps" was the old idiom which turned into a computing term which was a sort of start up protocol where the initial steps loaded additional functions which in turn could be used to get a full suite of functions for an operating system going.