The ever-increasing demand for intelligent, automated, and connected mobility solutions pushes for the development of an innovative sixth Generation (6G) of cellular networks. A radical transformation on the physical layer of vehicular communications is planned, with a paradigm shift towards beam-based millimeter Waves or sub-Terahertz communications, which require precise beam pointing for guaranteeing the communication link, especially in high mobility. A key design aspect is a fast and proactive Initial Access (IA) algorithm to select the optimal beam to be used. In this work, we investigate alternative IA techniques to fasten the current fifth-generation (5G) standard, targeting an efficient 6G design. First, we discuss cooperative position-based schemes that rely on the position information. Then, motivated by the intuition of a non-uniform distribution of the communication directions due to road topology constraints, we design two Probabilistic Codebook (PCB) techniques of prioritized beams. In the first one, the PCBs are built leveraging past collected traffic information, while in the second one, we use the Hough Transform over the digital map to extract dominant road directions. We also show that the information coming from the angular probability distribution allows designing non-uniform codebook quantization, reducing the degradation of the performances compared to uniform one. Numerical simulation on realistic scenarios shows that PCBs-based beam selection outperforms the 5G standard in terms of the number of IA trials, with a performance comparable to position-based methods, without requiring the signaling of sensitive information.Index termsvehicular communications; initial access; mmWaves; 5G NR; V2V; sidelink; 6G; beam-based communications I. INTRODUCTION Connected mobility is a flagship element of smart cities and a mandatory step in the evolution towards automated driving, to guarantee traffic safety, efficiency, user comfort and environmental sustainability [1,2,3,4]. Moreover, sales volume and market share of connected vehicles represent a radical breakthrough for telecommunication operators, unlocking new business models and strategies [5]. In this framework, vehicular communications represent the key technology to enable information sharing and thereby cooperation among road users, to augment the ego-vehicle sensing and control capabilities. The heterogeneity of envisioned mobility applications, spanning from driving-assistance to on-board entertainment [6], call for a vehicular network that is extremely reliable, fast and resilient.The European Telecommunications Standards Institute (ETSI) has identified connected services for active road safety and cooperative traffic efficiency, to be enabled by Vehicle-to-Everything (V2X) communications, either Vehicle-to-Vehicle (V2V) or Vehicle-to-Infrastructure (V2I), since 2009 [7]. Therein, the addressed use cases belong to the low levels of automation (levels 1 and 2, according to [1]), i.e., driver assistance and partial automation features. To en...