Owners need a budget before they pay for full design. The estimator works from a narrative, a sketch or a floor area, and from the cost of similar past jobs.
Example: a design-build contractor asks an equipment supplier for a budget number for a new high school gym. No equipment spec exists yet.
State your assumptions in writing. List what you included, the quality level you assumed and what you left out. Label the number as a budget, not a bid. Update it when the drawings arrive, because the scope will change.