You guys are awesome. I will try all of your suggestions and try to figure out which one makes the most sense.

Now I have to figure out who is going to pull me out of bed at 5AM. lol

5:30 in the AM I would get on Baldwin (it will change to Webster) than get onto Palisades anywhere from Ravine North. Right at Paterson Plank and then go on the 14th St Viaduct.
I do this frequently at 6:30 AM. Can't remember anytime had any problem, even on the viaduct.
Later in the day I might do the elevator at Congress if I were going to 14th St, but at 5:30AM for me it's a no brainier, use the Viaduct.

Death-defying as it is, I take the Palisade>Pat Plank>14th Viaduct route on the regular. I think it'll be the fastest route for your trip. Be prepared to use your arm to beat on the hood/sides of the Bergenline vans as they try to pin you to parked cars on the narrow section of Palisade Av. Cars on the viaduct like to fly and even when there's plenty of room to pass, many seem to prefer to lay on the horn and yell at you instead.

The waterfront route CatDog described is prettier and safer, but it's not a quick zip. Also, you're required to dismount and walk through the Hoboken Terminal area, which is not good if you're wearing cycling cleats. But Sinatra Dr is a good route once you're in Hoboken.

A good alternative might be Hoboken Avenue as Jumba recommended (I've never used it on a bike, so can't vouch) and then zig-zag to Observer Highway. Observer carries a lot of traffic, but it's not too bad on a bike, just mind the potholes/bad patches. And then use Washington>1st>Sinatra.

I'd go down Newark all the way to Exchange Place and then bike along the waterfront over the Newport Bridge, and stick to the waterfront in Hoboken all the way to 14th st. Beautiful ride, and the safest possible route, since you're barely in any streets.

Head down from Palisades Ave to Hoboken Ave. Stay to your extreme left, and then right as you make left onto HA. You are travelling against traffic but the street is wide. Once in Boken stay as far west or east(depending on your destination on 14th) as possible.

The 14th bridge is a bit of a drag-strip at most hours, and has very narrow lanes due to ongoing bridgework. At 5:30am it might be ok, but best to avoid it if possible.

Two alternatives: turn right off Palisade to Congress St and use the 9th St Light Rail elevator to get to Hoboken. Or turn left off Palisade to Ravine, then left again down NY Ave. That will bring you to Observer. Streets like Clinton have fairly good bicycle lanes to get you to 14th St.

I am considering training with a group of cyclists and they start on 14th Street in Hoboken in the early morning hours before work.

Does anyone know a good, safe, quick route from Journal Square to 14th Street in Hoboken.

When I ride to liberty state park I go down Newark ave but I wonder if its safe to ride down Palisade to the 14th street bridge and go that way.

I would be biking around 530 am.

Let me know your thoughts.