One of my pet peeves is people misusing the word 'encounter' in theological and religious contexts. 'Encounter' in English means one of two things:
(1) A casual meeting, usually brief and usually by chance
(2) A direct hostile interaction between disputants or enemy forces
If you are focused on 'encounter with Jesus', your standards are too low. What people mean when they such things is not 'encounter' but friendship or charity or love. If you mean that, say that.
The problem has become worse recently because Pope Francis likes to talk about encuentro and it gets translated by 'encounter', which in this context is a false cognate; the Pope uses the Spanish word to indicate deliberate acts of solidarity, which is not what the word 'encounter' describes (and by experience talking with people, I am very certain is not what is conveyed to most English speakers by that word, since they can tell from context that it is supposed to be more than a casual meeting but they have no idea what). Deliberate acts of solidarity. That is what the English translations should convey.
ADDED LATER: Incidentally, if you want to translate encuentro as literally as possible, 'finding' is infinitely better than 'encounter'. Not 'encounter with Jesus' -- finding Jesus. Not 'encounter with your neighbor' -- finding your neighbor. Better than that, 'going out and finding', both sides of which the Pope often explicitly emphasizes. Encuentro used of persons is still capable of being stronger and more active than 'finding', but the gap is far less, because 'finding' is a much stronger and more active word than 'encounter'.