Tide beats time of day here, which is the one piece of advice that changes people's visits. The mudflats feed birds when they are exposed, so a falling or low tide concentrates herons, egrets, ibis, willets and plovers onto a shrinking table of mud. A high tide scatters them into the mangroves and can make the same route feel empty.
Season stacks on top of that. Winter — roughly December through March — is peak, when migratory birds are on the islands and the resident population is joined by everything that has come south. Roseate spoonbills are the species people come for, and they are most reliable in the cooler months; white pelicans turn up in winter in numbers; reddish egrets work the flats in their unmistakable lurching style.
Beyond birds, the refuge holds alligators, river otters, bobcats, raccoons and marsh rabbits. Otters and bobcats are luck rather than planning.
Practical framing: dawn and the two hours before dusk are the active periods, and the combination you want is an early-morning low tide in February. If you can only pick one variable, pick the tide.