Are fellowships harder to get into the longer you’re out of school?

Most fellowships I’ve seen require application within a certain timeframe after graduation. I’ve now been practicing for two years and considering a specialty change. But I feel like doing so would be challenging without some additional training. However, I have no means of accessing past transcripts, nor do I have any faculty that I’ve kept in contact with, which would make acquiring a LOR challenging. I feel truly stuck in my specialty and since it’s all I know, leaving would be a significant relearning curve and likely come with a pay cut.