さっき + [sentence] さっきの + [noun] さっきから / さっきまで + [sentence]
さっき means "a moment ago", "a little while ago": earlier today, usually within the last hour or so. It is a time word like きのう昨日, so it takes no particle and sits at the start of the sentence or just before the verb.
On its own, さっき puts the event in the past, so the verb is past too: ×さっき行きます.
With から and a ~ている verb, the action started a little while ago and is still going on. With まで, it went on until a little while ago and has stopped.
With の, さっき describes a noun: the one from a moment ago.