The COVID-19 vaccines are not experimental. As with all vaccines allowed in the US, they underwent strict and comprehensive clinical trials.
The safety measures and approaches taken during COVID-19 vaccine trials were the same as those used in trials to approve other vaccines.
No steps were skipped, but some steps were conducted on an overlapping schedule to gather data faster than usual.
Additionally, the mRNA technology for the Pfizer and Moderna vaccines may be newer than some previous methods, but it is not new. Scientists have been working on mRNA since the early 1990s. Research on the SARS virus in the early 2000s also helped lay the groundwork for COVID-19 research.
https://www.bu.edu/articles/2021/myths-vs-facts-covid-19-vaccine (Boston University)