Firstly, have you checked with your local council as to requirements for structures of this type? There may be limitations on the area of a pergola.
Secondly, is this pergola common property? If so do not touch this without permission. You may not only be in breach of council regulations but of strata by laws as well. You would need permission and no doubt an exclusive use clause.
If the structure is not common property, you could put in a submission via the managing agent to the EC/OC (don't give it to them directly – your word against theirs as to whether they received any info). Going via the managing agent leaves a “paper trail” and makes such a request official ie there is a record of it. Leaving for the EC in the letterbox or under the door you have no proof.
Include in your submission any details about council regs (whether complying or non complying development) current square metres, how many square metres the finished pergola will be. Include diagrams, measurements, materials used. Assure EC that only licenced insured tradespeople will be used. Any damage to common property will be rectified (from delivery of materials for example), tradespeople will work within defined hours to limit noise to neighbours. Just include everything and anything.
But whatever you do, don't go ahead and just do it because you haven't heard back either way.