You’re bumping up against the idea that Audacity doesn’t do any production in real time. You can do that later in Post Production combining a live performance and a pre-recorded clip using the Overdubbing feature, but you have to stop what you’re doing and set it up that way. I know of no way to get the first clip in Overdubbing Mode.
You could try setting up Overdubbing with a prepared silent track instead of rhythm or backing. The first music track you record will then sound like the first track when you play it back, but it will really be track 2. Overdubbing plays back all existing tracks (unless you stop it) every time you press record.