That is not what is done usually. Data can be non-normal in many different ways. Two common measures of non-normality are skewness and kurtosis, but a data set might be non-normal and still have zero (or non-significant skewness and kurtosis), such as a bath tub (symmetrical twin-peaked) distribution.
The usual way to continue when you establish evidence of non-normality is to use a nonparametric statistical test that does not assume normality, or check the robust exceptions of the equivalent parametric test as sometimes they can work reliably even when the data is non-normal. Please refer to my study guides for more information.