If you were to develop a new scale, the answer is 'no.' See:
Article Developing and Validating a New Multi-Dimensional Scale for ...
If you were to assess an established measure validity start with CFA. If it fails to fit your data, do EFA and redo CFA using the new structure for confirmation. See:
Article A Confirmatory Factor Analysis for SERVPERF Instrument based...
EFA is normally used for questionnaire design, that is, it is used for analyzing responses from questionnaires you designed for the purpose of establishing latent factors forming a scale you desired. CFA is used for analyzing responses from pre-establised questionnaires, which had internally reliable scales established with earlier rounds of EFA. So if you are using some pre-existing questionnaires/surveys and you want to find out whether your collected responses yield the same factors/dimensions as found by the original authors, you need to apply CFA. If you are designing a new questionnaire and pilot-testing new items, you need to apply EFA to establish the factor structure first. You can refer to my papers for examples of both types of analyses.
It is not recommended. The correct thing is to observe how the items are grouped in the Exploratory Factor Analysis. Then, with data from another sample, confirm that the items have good parameters with Confirmatory Factor Analysis.