Help with Exploratory factor analysis


I am running exploratory factor analysis (EFA) to explore the existence of possible structures within my sample and I have managed to extract 6 factors. Would it be correct to state that since by means of EFA I have managed to see structure within my sample, I hypothesize that correlations exist between the variables in the sample, and then proceed to another form of analysis to test this hypothesis in more detail?
I am only interested in using EFA as a first step for analyzing the underlying structure within my sample without assuming the existence of any correlations.

Thank you very much for your help.