On this topic, the OP replied writing
Killing 2 birds with one stone would make sense
The same saying in Italian, my mother language, sounds as "Prendere due piccioni con una fava", which may be literally translated as " Catching two pigeons with one broad bean".
No matter if you are catching or killing them, we have a couple of birds involved in both languages.
Another Italian proverb is "Il mattino ha l'oro in bocca", literally "Morning has gold in its mouth", which English version is (AFAIK) "The early bird catches its worm", that it's totally different.
I wonder if there's a common logical / idiomatic substrate for certain proverbs or if similar ways of saying are mere coincidence....