At this FAQ page of German Federal Office for Migration website, it is stated that you can apply for an approval for change in your employment with no extra conditions than your initial application.
About your specific situation, where you had not even started working with your employer who sponsored you for your EU blue card; it is also stated in the last sentence that you can still apply if your issued Blue Card is terminated 'prematurely'.
Question: From what point in time may I change employers?
Answer: Any change of job during the first two years of employment requires the approval of the immigration authority (section 19a subs. 4 of the German Residence Act). Approval is subject to the same preconditions as initial issuance. If the minimum gross salary threshold has been raised during the intervening period, compliance with the new threshold must be proven. Holders of an EU Blue Card are obliged to inform the competent immigration authority if the employment for which the EU Blue Card was issued is terminated prematurely
By the way, as someone in same situation at the moment, I am extremely curious how you went through the process, from getting an appointment to approval. I would appreciate if you can give some details about authorities' opinions of this premature change, possibly with a comment or edit.