Conventional Topology Optimization (TO) enables the inverse design of nanophotonic structures by specifying the objective and constraints without a predefined topological concept. Yet, extreme scenarios such as the design of a lightsail pose challenges that require new solutions. Here, a convolutional neural network (CNN) based TO methodology is extended to optimize a two-dimensional photonic crystal used to design a lightsail that aims to reach the nearest star (Alpha Centauri) within 20 years by achieving 20% of the speed of light. The CNN-TO performance is compared to a more conventional method of moving asymptotes (MMA) based TO by optimizing a photonic crystal unit-cell for the 2016 Starshot Initiative parameters. The CNN-TO requires up to 40% fewer iterations than MMA-TO to reach better performance under different operational conditions. The generated design turned out to be easy to fabricate, allowing them to be produced with optical lithography. Additionally, a study regarding the design challenges of the lightsail has been performed, which resulted in an optimization considering the functionality of the sail. Additionally, the study showed the sensitivity of the resulting design to varying objectives and materials. Therefore, underlining the necessity of considering multiple operating conditions (e.g. laser alignment and cooling) within the design process.