If you have the accepted values for all model fit indices and reliability & validity generated from CFA, you can run SEM soon after that for testing your hypotheses.
"Ideal" is not the best word to use in describing your issue. CFA is obvious first step in your analysis as if the results for CFA are compromised (see Khan arguments) you should stop at this point.
you should be having a theoretical model to to run SEM whereas CFA is done to confirm exploratory factor analysis so for CFA you need bot be having a theoretical model.
The usual procedure to test two aspects of your theoretical specification. First, CFA to test the "measurement model" in terms of the assignment of items to your latent variables (i.e., factors). Then, after you develop that measurement model, you proceed to testing the "structural model" by assigning relationships (i.e., paths) to your latent variables.