Sometimes тихо can be translated "cautiously". I would suggest "The more cautiously/carefully you go, the farther you'll go."
Compare with "Slow and steady wins the race" -- that's the usual English phrasing for the moral of the Эзопова басня про черепахи и зайца.
Also compare with the expression (быть/жить) тише воды, ниже травы -- literally it's "(to be/to live) quieter than water, lower than grass," but "to maintain a low profile" would also be a good translation, in some contexts.