A light year is near enough to 10^16 metres and the age of the Universe is about 10^10 years making the Universe in the order of 10^26 metres in diameter.
The smallest meaninful distance (Planck's Length) is about 10^-35 metres. A human is about 10^0 metres.
So you see on the scale of things there are nine orders of magnitude more below us than above us. Hence I conclude the Universe is not really all that big.
That sounds like a reasonable worry. Certainly no-one can gainsay it.
But if as said, the universe is 14,000 million years old and your span is 70 years, then the chances of it happening while you're around is about 1 in 200 million ... that's assuming it hasn't already happened and no-one knew about it.
Probably more likely to get mugged by a comet 10 minutes after collecting your lottery winner's cheque.
The idea of colliding with another universe is taken seriously by cosmologists. There is nothing that says it couldn't happen. We don't really know what the overall framework is like behind the universe.
In fact a vast empty volume has been found where there are no stars at all. Such voids should not be possible in current cosmological theory. Some schientist have concluded that such anomalies are explained by interactions with other universes.