Thank you for clarifying.
There is no law that entitles a plaintiff to postpone the CMC because the complaint has notyet been served. In fact, the law requires the plaintiff to serve the complaint within 60 days of filing it unless the plaintiff can demonstrate "good cause" for failure to do so. So, the law would not permit a plaintiff to benefit from their own violation of this rule by pushing back the CMC because they have not yet served the complaint. In fact, one of the very core functions of the CMC is to determine what progress has been made on the litigation, and one of the very issues the CMC will examine is why a complaint has not yet been served if indeed that is the case.
The rules do provide a limited ability to reschedule CMCs, though. Here's what the court says:
Parties desiring to reschedule a CMC, notwithstanding the above, are to either:
1) File and serve a stipulation executed by all parties and appear ex parte in the trial court; or
2) File a fully-noticed motion with the trial court requesting the CMC be rescheduled.
Here, your only option would be to file a noticed motion, which you would have needed to do several weeks in advance of the CMC. So, at this point, you really just have to show up at the CMC and explain why the complaint has not yet been served and what you are doing to advance the case. Since you are pro se, it is unlikely that you will be sanctioned for failing to to serve the complaint within 60 days. Most likely, an order to show cause will be scheduled at some point in the next few weeks at which you will be asked to explain why you still have not served the complaint if you do not file a proof of service by the hearing date for the OSC.
I hope this clarifies things. If I can provide any further assistance just let me know.