Sound sources should decay with distance(though less than real world, to create better feedback) and should arrive after N milliseconds dependent on delay.
In general the sound delay should not exceed visual display for more than a few seconds: the world distances should be more "compressed" and seem closer(as player wants more feedback over the game state).
Instead of quadratic decay(inverse square), the better way is to use inverse diminishing returns formula with sound slowly losing power with 100% to 0%.
Distance delay for sound can also be calculated with diminishing returns formulas as growing to max of 10 seconds or 100%.
In general there is no need for loud sound at close distance, the decay with inverse diminishing returns is good enough to represent distance to sound.