Legal Question in Construction Law in California

Absolutely not. You have described a classic design-build contract. The architect and engineer in this situation are subcontractors to the general contractor. That makes the general contractor responsible for their errors, not the owner. When the owner hires the design professionals and then provides the plans and specifications to the contractor who will build the project, there is an implied warranty from the owner to the contractor that the plans and specifications are correct and buildable. It is a term of the contract that the law imposes on the contract even if it is not stated in the contract. That law absolutely does NOT apply in a design-build contract. In design-build, the contractor is obligated to provide a finished result, built to code and passing all inspections. The owner has no responsibility for errors or omissions in the design.

If by "hired" you mean that the contractor "selected, instructed, retained and paid" the architect and engineer, I'd say you are the clear winner in any lawsuit of arbitration over this metter.