There are two ways to proceed. If you're already talking to or working with a contractor, ask the contractor whether you'll be able to get permits using the existing plans without further involvement of an architect. Alternatively, take the plans you have in to the planning department help desk and see what they have to say.
In addition to the technical issues involved in adding a floor to an existing structure, there are other potential hurdles such as the "311" process which involves notifying neighbors if your plans trigger that requirement.
Prudential California Realty
The best way is hire a architect /engineer even you want to have minimal change from the previous plan. Also the engineer can submit the plan to the city for you, and if you have questions regarding the plan you need a good engineer. I am working with a architect/engineer is pretty good, you can message me if you want to have his contact info.
First, it is very good that you wrote in to ask this question.
The previous owner did not get permits to do this work. I highly advise that you do this if you want to do it "right". Although very common for people to do work without them, when it comes to resale, people will weigh this regarding their decision to buy. If it's not to code, etc., the new owners may have to completely remove it or do work to bring to said codes. Ultimately, knowing the work is done correctly should give you peace of mind.
A good architect is important. They are important not only because of their skill in knowing how to do the job right but also because they have the contacts to get permits quickly. Always hire a qualified professional for any work done to your home.
Good luck and let me know if you need any referrals for architects in the area.