Systems and methods are disclosed for random access in a wireless communication system such as, e.g., a wireless communication system having a non-terrestrial (e.g., satellite-based) radio access network. Embodiments of a method performed by a wireless device and corresponding embodiments of a wireless device are disclosed. In some embodiments, a method performed by a wireless device for random access comprises performing an open-loop timing advance estimation procedure to thereby determine an open-loop timing advance estimate for an uplink between the wireless device and a base station. The method further comprises transmitting a random access preamble using the open-loop timing advance estimate. In this manner, random access can be performed even in the presence of a long propagation delay such as that present in a satellite-based radio access network. Embodiments of a method performed by a base station and corresponding embodiments of a base station are also disclosed.