Especially in the old days of vinyl (when none of the fancy FX stuff was around) you’d be looking for tracks with an abrupt ending (like a clear last bang on the drum) and/or tracks with a snappy start (especially known tracks where the first one or two notes would already bring the aha! feeling with the crowd). After the last bang, count to 4 (creating your own mini-break) then on the 5th count hit play on the new tracks which you have obviously cued up to the first downbeat and off you go.
Point here being, not everything needs to mix. Silence can be a powerful friend in these situations.
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