There's no set time that's good to work out.

If 4:30 is what works for you then go for it!
As long as you're awake and able to put a good amount of effort into it.

From personal experience, I'd have to say that I prefer mornings. I like to get going ... but evenings are also helpful for de-stressing. So, it's really personal preference (which can change over time).

As Maddie stated.

It's all in your mind, if you naturally think "oh I feel like I get the best work out in the morning", you are mentally prepped to do your best then.

There are some variations of metabolic rate differences depending on whether or not you just woke up, etc, but nothing substantial that would largely improve your performance from my knowledge. Unless you have a specific schedule that may affect your performance, (i.e. you have a physically arduous job and you have to decide whether its best to work out before or after), no biggie.

4:30 a.m.? Are you getting enough sleep? I never cared much for getting up and working out early (7-8 a.m.), but have done it
on occasion. Most of my workouts have been past noon, but that's
just me. But if these wee hours work for you, I don't see anything
wrong with it if you stick with the schedule, then again, it might seem
to work against the body's natural 24-hr cycle over time.

I usually escersise in the evnings from 6-7 pm and i feel good - i think that's most important.

ive been told that working out earlier in the morning/day increases your metabolism for the rest of the day...but as everyone else said it just matters that you work out period...if you cant do it at 4am one morning but later on in the afternoon works better then do that...i've just been told that morning is better

I usually like to work out at 10am, the noontime heat hasn't hit yet so I won't sweat too much, but I've been awake for long enough to get blood flowing to all my muscles.

I learned from wii fit that it is easier to burn calories earlier in the day so it's best to eat a big breakfast and exercise the earlier the better