Good question! If interpreted literally, in theory this phrase does not rule out the possibility that the event might happen at some point later on. However, in practice, if someone says, ''That's not gonna happen any time soon", it's usually clear that the speaker thinks that it will probably never happen. In effect, this is a kind of understatement - one of many cases where what we 'say' is not exactly the same as what we 'mean'.

Consider the sentence "We won't be going on holiday anytime soon". In this context the speaker is suggesting that it will likely be a long time before they take a vacation, probably because they have a lot of work or not enough money. However, they would like to go on holiday and probably will at some point in the future. However if we imagine someone has broken their leg whilst skiing, we may ask them "When do you think you'll go skiing again". They could reply "It won't be anytime soon!". Depending on their tone and the situation, they could mean literally 'a long time' or that they don't plan to ski ever again!

it often means, "no"