Cooley was born to William, a master mason, and Mary Cooley in
London, and was baptised on 11 July 1742. He began his career as a carpenter apprenticeship in 1756 with interest in architecture under George Wright at first, then the master joiner in the office of works, William Greenell. Cooley worked as a
draughtsman and clerk to the architect and engineer
Robert Mylne (1733–1810), while the latter was building
Blackfriars Bridge in London, between 1761 and 1769. In 1769, he won the competition to design a new Royal Exchange in Dublin, and the building, now the
City Hall, was completed in 1779. The design shows the influence of Mylne's work, which in turn derived from French neoclassical architecture, with some accusations that Mylne refined the design or otherwise influenced the choice of Cooley as the winner. ==Architecture career and Ireland==