A great deal of coins started this way, that is, they started small and even on smaller exchanges while gradually improving their platform, building their products, use case, services, all of which they leveraged on to gain more users thus going for bigger exchanges which also leads to more volume. The major difference between now and then is that, then, most team are committed to their goals but nowadays only a few team are committed and of course their coin have good volume while listed on different exchanges as well. So to answer your question, yes it is possible but requires a lot of effort and patience from the team.