There is natural immunity and people can get reinfected.

After getting Covid your body still has and knows how to make Covid-19 antibodies, but this deteriorates over time.

This October 2021 paper on the durability of natural immunity against Covid-19 reinfection found that you can get Covid again as soon as 3 months after recovering from a case of Covid-19, and if the disease became endemic, the median person would get re-infected every 16 months. It’s worth noting that as this paper was published in October 2021 they were looking at Delta, not Omicron, which could change the numbers significantly.