The infected population is going to be statistically a bell-curve, with the extremes at either end. Antibodies are developed when your body detects an infection, and not before. Unless, of course, you take a vaccine that gives you the deactivated virus so that your body can begin creating antibodies before actually contracting the virus. When you eventually do come in contact with the virus if you have been vaccinated beforehand then you have developed antibodies to fight off the virus. Otherwise your body will start creating antibodies the instant it comes in contact with the virus.
The majority of viruses are brand new and never encountered before, or they are mutations of existing viruses that we have encountered before. In the case of mutations, a vaccine may or may not work. In the case of a brand new virus, like SARS-CoV-2, then it will take some time to develop a vaccine. There was a time when SARS, MERS, and H1N1 were brand new as well. New viruses have a tendency to pop up from time to time.
If they are showing symptoms then they are, by definition, not asymptomatic. Asymptomatic carriers are carrying the disease/virus without showing any symptoms whatsoever. They feel perfectly fine, but are still carriers of the disease/virus and potentially contagious. Asymptomatic carriers are extremely rare.