don't even

"They don't even know when this nation was established".

Как переводится?

Они даже не знают.

don't even = даже не (this is a pretty widespread option)

So, does this mean that
"Don't even think about it!"
would translate as
"Даже не думайте об этом!"
???

exactly!

"Даже не" is sort of "flat", emotionless, formal.
A way to emphasize or add some extra emotions to it is to insert "И" in between "даже" and "не".

Даже и не думай об этом!
Они даже и не догадываются о том, что наступил 2015 год!