From that we don't get how long it was between the time the Valiant left Earth, until the time it "disappeared." Couldn't have been too many years, but still maybe not immediately after departure.
...It's only later, when we learn that the episode must have been taking place in the 2260s, that it becomes necessary to assume that the Earth-> disappearance must indeed have been very
short, at most two years by modern reckoning.
At the time the pilot was being written, the writers probably were thinking the action was taking place at least three centuries after mankind reached the stars. (Okay, possibly. Or possibly even probably.)
Nor do we get any sense of how long it was between the time of the Valiant's disappearence, and when the Valiant arrived at the energy barrier.
I wouldn't word it quite that strongly. Spock does say the recorder marker was launched "200 years ago", to complement Kirk's "missing for over two centuries". So "decades" is possible, but "less than 50 years" would really be an upper end here.