Is it normal that i start dreaming immediately after falling asleep?

For as long as I can remember, I’ve always started dreaming shortly after falling asleep. Like within seconds. I know this because there’s been many times where I’ve only been asleep for 2-5 minutes and I’ve had vivid dreams. Sometimes I’ll even start dreaming before fully falling asleep and it’ll startle me awake. Just wondering how normal this is because it was my understanding that dreams don’t start until REM sleep which happens later in the sleep cycle.