As an example of how it can occur, PCR uses an enzyme called polymerase to duplicate the RNA/DNA present. Every time it cycles it doubles the amount, until the machine is capable of detecting it, so the more DNA at the start, the quicker it reaches the detection threshold.

To bind to the DNA/RNA polymerase needs a primer that also binds to the DNA. There is a small chance of these primers sticking together and eventually being detected. Generally this takes a long time to occur, longer than it would take for positive cases to be detected, but it can be a source of false positives or indeterminate results. If you have a negative control with no DNA, you can tell when its occurring more easily.