The ground-state functional corresponding to a closed bosonic string is derived by using the path-integral approach for the simple compact topology of a finite cylinder. This functional integral satisfies the ''no boundary'' Hartle-Hawking prescription and, therefore, we consider it as a candidate to describe the quantum state of the very early Universe. In light of this result and some thermodynamical considerations, the initial conditions of a stringy universe and its low-energy limit are discussed.