I hold the top underwater downside up and tap it against the ceramic piece before assembling it underwater.
I'm pretty sure that you will find that a pipette or syringe will get a LOT more air out even after you do this. The design of the lid traps air all of the way around the inside by the threads, and the only way that you are going to get it out is by flushing it out.
I buy 10ml oral medication syringes and use them for adding liquid amendments to my nutrients, flushing out the Blumat caps and a bunch of other things. You can buy them for anywhere from 15 cents to 50 cents apiece in quantity (Amazon, pet med suppliers, etc.) and they last a hell of a long time if you rinse them out. I bought a sack of 20 of them about 5 years ago and still have over half of them left - the only reason that I get rid of them is that the markings eventually wear off.