There is no scientific evidence that COVID vaccines create new variants or cause them to emerge. New variants happen because the virus that causes COVID constantly changes through a natural ongoing process of mutation (change). Even before the COVID vaccines, there were several variants of the virus, and more variants are expected to emerge.
In truth, COVID vaccines can help prevent new variants from emerging. As it spreads, the virus has more opportunities to change. High vaccination coverage in a population reduces the spread of the virus and helps prevent opportunities for its mutation. The CDC recommends that everyone 5 years and older get vaccinated as soon as possible.
SOURCE: https://www.cdc.gov/coronavirus/2019-ncov/vaccines/facts.html (CDC)