An independent determination of cosmological parameters is important to ascertain the possible need for new physics beyond the standard cosmological model and to have better control over systematic uncertainties, given the tensions in current cosmological parameter measurements. This work focuses on finding and studying the physical properties of HII galaxies (HIIG) observed by the JWST and provides cosmological constraints using a single-distance estimator over a vast redshift range (0 < z < 13). HIIG are young outbreaks of star formation with spectra showing intense emission lines. Thanks to them and the use of the distance estimator based on the established correlation between the Balmer emission line velocity dispersion and luminosity for HIIG, we can constrain cosmological parameters with high precision. In this talk, I will show the results obtained with this program, highlighting the JWST data.