Ammonia zero + Nitrites zero = tank cycled.
Water from the gulf may have nitrates, but if you have some means for nitrate export in your system (algae scrubber or refugium, Jaubert plenum, DSB, coil denitrator, etc., and I make no endorsement of any of the above methods), it is possible for you to have zero nitrates. I have undetectable nitrates on my test kit (colors at 0, 5, 10, 20, etc. ppm).
Some folks may have an excessively sensitive test kit, which can detect, say, 0.01ppm ammonia or 0.01ppm nitrites, in which case, you may never get to a zero reading. Because anything which metabolizes will generate ammonia, and your nitrifying bacteria will never scrub ammonia to zero; they'll scrub them to undetectible (unless you have the ultrasensitive test kits).
I'm traveling, and my internet connection is flaky, so I may not be noticing posts mentioning me immediately. Sorry if that's an inconvenience.
Regards,
Hy