The growing number of applications of Fluorescence Intensity Distribution Analysis (FIDA) demands for new approaches in data processing, aiming at increased speed and robustness. Iterative algorithms of parameter estimation, although proven to be universal and accurate, require some initial guesses (IG) of the unknown parameters. An essential component of any data processing technology, IG become especially important in case of FIDA, since even with apparently reasonable, and physically admissible but randomly chosen IG, the iterative procedure may converge to situations where the FIDA model cannot be evaluated correctly. In the present work we introduce an approach for IG generation in FIDA experiments based on the method of moments. IG are generated for the sample parameters: brightness, concentration, and for the parameters related to experimental set-up: background, observation volume profile. A number of analytical simplifications were introduced in order to increase the accuracy and robustness of the numerical algorithms. The performance of the developed method has been tested on number of simulations and experimental data. Iterative fitting with generated IG proved to be more robust and at least five times faster than with an arbitrarily chosen IG. Applicability of the proposed method for quick estimation of brightness and concentrations is discussed.