With Beatgrids enabled, you can set Serato to start playback from the first beat marker. Anything else would require directly editing the tracks themselves which is not the job for a DVS.

You can go one stage further and set serato to play from the first cue point.

For background songs I have made FLIPs to help with what you are asking for. At a set point on an out going track, the playhead will jump to the very end of the track. When used in conjunction with "autoplay"and "play from first cue", this cuts out the dead space at the end of a track, loads the next track with the flip already armed, skips all the dead space at the start of the track and plays from the first cue. Works perfectly for background music.