There is no specific minimum population size required for preserving modern civilization and advancing it further, as several factors contribute to the sustainability and progress of a civilization. These include access to resources, governance and leadership, education, scientific and technological progress, economic stability, and social and cultural norms, among others.

However, a minimum viable population (MVP) is considered to be the smallest number of individuals required for a population to survive and avoid extinction. The exact number required for an MVP can vary depending on the species and its environment, but a commonly cited estimate is around 500 to 1,000 individuals.

For human populations, the MVP is a topic of much debate and speculation among demographers, biologists, and sociologists, with estimates ranging from a few thousand to several tens of thousands. It is important to note, however, that an MVP is not a guarantee of a thriving civilization, and much larger populations are likely needed to support the complex systems and institutions that make up modern civilization.

In any case, it's worth considering that population size alone is not the only determining factor for a civilization's success and that a more diverse, equitable, and sustainable society is likely to be more resilient in the long term.