It is demonstrated that a thin dense plasma slab (lens), placed before a multi-centimeter-length, low-density plasma (accelerator), overfocuses an incident petawatt laser pulse at a controlled location inside the accelerator, creating an expanding electron density bubble that traps plasma electrons over a brief time interval. As soon as the pulse stabilizes and self-guiding begins, the bubble stabilizes and transforms into the first (non-broken) bucket of a conventional three-dimensional nonlinear plasma wave, eliminating any chance for further injection. A well collimated, quasi-monoenergetic electron bunch with a zero low-energy background further accelerates to a multi-GeV energy.