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I would approach this in two ways:
Top down
and
Bottom up
Top Down (Project First) With this approach, the project will set the limits of my estimate - simply because projects, more or less, have launch dates. I will fit my design process on the available timeline. Will take some shortcuts, drop some steps in the process. Will fit the estimate within the threshold of non-compromise.
Bottom Up (Process First) With this one, the design process is prioritized. The project timeline is defined by how long the design process will take.