The great thing is that the next time this happens, a vaccine can be created equally quickly.
In another infection, your cells still get infected, but the infection is just stopped very quickly. HIV has inscription and reverse transcription enzymes in it, so it can actually glue its sequence into your DNA. It changes your DNA enough to replicate it, but not enough that your cells change their structure so your immune system can't recognize them as infected (and those changes can cause your immune system to fail over time: AIDS).
Even if your body is primed to deal with HIV infections, if the infection happens, it's already too late.
I'm not sure who antiviral drugs like PREP work, but you'd need something like that permanently in your system.