We explore the possibility of constructing a string model of the early Universe. Our model assumes an intuitive picture of the string era of the Universe, the dominance of a single long string, as suggested by string thermodynamics. We argue that, irrespectively of the precise initial condition, the system evolves such that it approaches the scaling era in which the long string, the loops, and the radiation coexist with roughly equal weight. The scenario is based on the notion of the scaling solution obtained in the study of the evolution of a cosmic-string network. Unlike the cosmic-string case, however, there exist self-consistency conditions one of which relates the motion of the string in a classical background geometry to the structure of space-time itself. The other determines the effective number of light degrees of freedom for given fundamental constants in string theory. Interestingly, our scenario offers an explanation of the origin of cosmic entropy: it has been stored in the complex structure of the cosmic fundamental string.