One of the main drivers for new waveforms in future 5G wireless communication systems is to handle efficiently the variety of traffic types and requirements. In this paper, we introduce a new random access within the standard acquisition procedures to support sporadic traffic as an enabler of the Internet of Things (IoT). The major challenge hereby is to cope with the highly asynchronous access of different devices and to allow transmission of control signaling and payload "in one shot". We address this challenge by using a waveform design approach based on bi-orthogonal frequency division multiplexing where transmit orthogonality is replaced in favor of better temporal and spectral properties. We show that this approach allows data transmission in frequencies that otherwise have to remain unused. More precisely, we utilize frequencies previously used as guard bands, located towards the standard synchronous communication pipes as well as in between the typically small amount of resources used by each IoT device. We demonstrate the superiority of this waveform approach over the conventional random access using a novel mathematical approach and numerical experiments.