Plan a gradual build-up by prioritizing purchases spread over x years.
Demonstrate cost-savings to gain support for increased funding. For example, NUL has reciprocal borrowing privileges with the University of Chicago and Loyola University. After a collection assessment establishes what NUL does not have, priortize purchases... if the title is secondary, you can demonstrate cost-savings by listing it as something that will not be purchased due to reciprocal-privilege agreements.
Establish a "core" collection up front.
Prioritize purchases using variables such as: publication date and what is held in benchmark libraries.