From what I’ve read, most of the length of time to vaccines approved is due to regulatory red tape and logistical issues, all of which were removed or limited, which sped up the process significantly. Also, long-term side effects of vaccines are typically known within a few months, and the mRNA vaccines underwent the required testing periods. The mRNA technology has been around for at least a couple of decades, iirc, if not since the 80s, which allowed its use in these vaccines so quickly.
Us average folk may never really know the full story. What we can say with certainty, is that it is not some depopulation conspiracy.