You can start and submit your application without a passport. Instead of the passport copy, you can upload the scanned copy of any document that may be used to prove your identity (e.g. your national ID card). In case you do not have any identification document before the application deadline, you can upload a signed declaration in which you state that you will obtain and upload the required document before 1 August.

Later though, if you are awarded with the scholarship, you will definitely need a valid passport in order to be able to enter Hungary.