Maybe this will help explain it.

Some interesting bits:

a normal sleep cycle has this pattern: waking, stage 1, 2, 3, 4, 3, 2, REM. Usually, REM sleep occurs 90 minutes after sleep onset.[/b]
Each subsequent cycle lasts longer, as its respective REM stage extends.[/b]
polysomnograms show wave patterns in REM to be similar to Stage 1 sleep.[/b]
I don't think anyone claims -- well, I don't anyway -- that you can't dream when you first go to sleep, only that it's more common to have your longer, more vivid dreams after you've slept a few cycles. And the usual caveat: everyone is different.