Certificate of British citizenship

Hello.
I am a Trinidad National and I have recently applied for British citizenship in May.

I am planning a trip to Trinidad in December and was hoping to also spend a couple of days in the US as well. If my application for British citizenship is successful I will probably get my Certificate of British citizenship in November, however I'm a bit concerned that I may not get my British passport in time for the trip. As a Trinidad national I need a visa to enter the US and I would rather not spend $160 to get a visitor visa unless that is my only option.
So my question is can I travel to the US using my Trinidad passport and also use my Certificate of British citizenship to prove my British nationality, therefore enabling me to travel without a visa?

Your certificate of naturalisation is not a travel document. If you don't have your British passport you will need a visa on your Trinidad passport.

Even with a British passport, you have to apply online for an ESTA before travelling.

British passports take about 3 weeks at the moment.