が is used with できました to describe that a building has finished being built. Who built it? We don't know. We just know it was built, thus が and できました is used because we're just describing something that simply is and not who did it.
で expresses the method that something is done, or, the manner in which the verb was completed. The speaker is requesting that the manner of speaking be louder, i.e,. 大きい声で... = "in a louder voice..." or "by method of a louder voice..."