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The article is devoted to the problem of reducing the time between switching on the navigation receiver and getting a navigation solution in the case when the available accuracy of the initial synchronization of the receiver’s time scale is insufficient for the implementation of a hot start scenario. An algorithm is proposed and mathematically justified that allows achieving the average waiting time for the first solution, typical for a hot start, when the conditions for a warm start are met. The novelty of the presented approach consists in the introduction of an additional time variable into the estimated state vector of the system, which allows solving the navigation problem even if it is impossible to calculate the pseudo-dalities of navigation satellites using classical methods. The use of the proposed algorithm opens up wide prospects for simplifying and reducing the cost of navigation systems, which is especially important in a number of special applications. The results of testing the described method on real measurements and in mass-produced products are presented.