The ability to switch off the internal combustion engine (ICE) during vehicle operation is a key functionality in hybrid powertrains to achieve low fuel economy. However, this can affect driveability, namely acceleration response when an ICE re-engagement due to a driver initiated torque demand is required. The ICE re-start as well as the speed and load synchronisation with the driveline and corresponding vehicle speed can lead to high response times. To avoid this issue, the operational range where the ICE can be switched off is often compromised, in turn sacrificing fuel economy. Based on a 48V off-axis P2 hybrid powertrain comprising a lay-shaft transmission we present an up-front simulation methodology that considers the relevant parameters of the ICE like air-path, turbocharger, friction, as well as the relevant mechanical and electrical parameters on the hybrid drive side, including a simplified multi-body approach to reflect the relevant vehicle and powertrain dynamics. Applying different ICE re-start strategies at different speeds and gears, the driveability of the ICE re-engagement was evaluated using a commercialized driveability evaluation tool. Subjective ratings, processed from the calculated vehicle and powertrain objective characteristics, finally enable to perform parametric studies to identify ideal ICE re-start strategies and to, furthermore, identify governing parameters like gear ratio, engine target speed and load, power and torque characteristics of the electric propulsion system as well as relevant stiffnesses in the driveline to enhance the operational range of the ICE start-stop area.