There's not a good deal of solid literature on it in English that I've found, but contemplative Christian prayer evolved later on. I want to say circa 500 or so. I think today it's primarily found in the Eastern Orthodox churches.
https://www.jstor.org/stable/3270411?seq=1
it connects silent prayer to Philo, a contemporary of Jesus https://en.wikipedia.org/wiki/Philo
and it connects silent prayer to early desert fathers, like Clement of Alexandria https://en.wikipedia.org/wiki/Clement_of_Alexandria
Also. For clarity (you may know this, but others may not) I want to distinguish very clearly the difference between a silent prayer and meditation.
A silent prayer is verbalized intention within your head, sometimes mouthed. If you were to look up Judaism's silent prayer, it is repeating a ritual sequence of words - the meanings of which you should know. As traditionally conceived, it is addressing the Eternal as a Person.
The different meditation approaches I've encountered - conventional "Western mindfulness" and a more intense secular Hindu system - are focused on detaching awareness. Sometimes mantras are used/repeated. It is exceptionally variant from the early silent prayer approach, or even the nominal silent prayer approach of today.
Contemplative prayer did start with the desert fathers, I think.