Use a comma after the introductory phrase.
The ellipsis doesn’t belong, but if you really, really want to use one anyway, at least begin the next sentence as a sentence: leave a space after the punctuation and capitalize the first word of the new sentence.
Three months ago, every other human being apparently vanished while you slept. Today you hear an engine in the distance.
(Alternate version with ellipsis: Three months ago, every other human being apparently vanished while you slept… Today, you hear engines in the distance. The comma after Today is not necessary — the introductory phrase is only one word — but it isn’t incorrect, either, so I included it to show yet another option.)