TL;DR: In the original timeline, Sarah Connor never knowingly encountered a Terminator until the events of the original film. It's impossible to say whether or not one was sent, however.
In the timeline of the original movie, Sarah has no idea that Terminators exist until Kyle Reese explains it to her. However, since her life until then is undocumented, it does not mean that a Terminator wasn't sent to kill her at a point earlier in her life.
A recurring theme in the Terminator comics by Dark Horse was that Skynet, having the advantage of hindsight, had used its time-travel technology to scatter Terminators throughout history. Many of them were sent on missions to ensure - or improve - the domination of SkyNet over humanity. Due to the prototype status of the technology, however, more than one Terminator found itself sent to the wrong time or place.
Although the Dark Horse comics aren't considered canon, we did see a couple of similar examples playing out in the live-action Sarah Connor Chronicles. Given that, it's entirely possible that a Terminator WAS sent to kill young Sarah Connor and either never arrived or somehow failed in its mission. With the limited information we have, we can only speculate.
For all we know, Sarah and her parents once witnessed a horrible accident where a man was crossing the street towards them and got hit by a bus, then an 18-wheeler, than a convoy of dump trucks and finally a street sweeper.