This is (surprisingly) not true. People do not pause between words, however when listening to a language that they understand, they do perceive pauses between words; even though such pauses do not exist.
I'm not a linguist; I don't know what the proper name is for the thing people do between each pair of spoken words—that they don't do inside words—but I do know that there is something people do there. I would call it "a pause" because that is the function it serves. It's an overlap of lesser "terminal" sounds that forms something that is detectably a semantic gap—like the pause between crossfaded tracks on a gapless record, or between movements in a concerto.
Whatever it is, it is there, because speech-recognition systems use it to detect spoken word boundaries regardless of language. (This heuristic does screw up sometimes; spoken language does often "slur" particular word-pairs together. But it's rare enough that these can be trained as specific exceptions to the rule, rather than needing to throw out the rule.)
Seems more productive (and enlightening to all) than the agree/disagree dialogue here.
The best way to see this is to try listening to a language you do not understand, and try to identify word boundries.
Indeed, the paper I link argues that some phonetic cue must exist because babies can recognise word boundries.
[1] https://www.sissa.it/cns/Articles/94_doInfPerceiveWordB.pdf
A monotonal, monotempo sound would not be able to make that difference audible