The title pretty much says it all.

What was the earliest level and time in game it took you to get to new vegas?

I tried going straight to vegas one of my playthroughs. Right after getting out from the doctor's office, I travelled north at level 1. I stayed to the west as far as I could, until I hit a whole bunch of cazadores. Victor showed up and tried to defend me like usual, and got completely decimated by the cazadores. But it bought me enough time to run and jump on to the side of the cliff, where the cazadores couldn't get me.
After about 2 minutes, all the cazadores took off trying to find a way up to me, and I continued forward. When I did jump off the cliff finally, a cazadore attacked me, and I managed to jump back on the rock, and kill him with my 9mm and like 20 bullets haha.
Anyway, killing the one cazadore leveled me up to level 2 instantly.

So I continued through the canyon north of goodsprings, and got attacked by the viper gang dudes in that little town. (the one with the special spiked knuckles in it).
Needless to say, I was killed like 3 times, by the dude with the trail carbine. (he could basically 1 hit kill me).

So I reloaded right after I killed the cazadore, and this time waited til night time. Once it was night, I managed to sneak around the town, and when I was almost around the trail carbine dude spotted me and started shooting. By some fluke, I managed to run away and get away from the gang, with almost no health left.
After that I continued to new vegas, snuck around the deathclaws and the fiends, and finally made it in to freeside.

Of course, I was level 2 with no money, so I couldn't get into the strip. So to get some coin, I ran into the van graffs and snatch and ran as fast as I could. I just ran into the middle of the room, and stole everything I could in 5 seconds and ran out before getting decimated. The van graffs chased me in the street, and eventually got killed by other npcs, then I looted their bodies for combat armor.
So then I went to the atomic wrangler, made some cash doing blackjack til I broke the casino and got kicked out, with like 15k in bottle caps now.

Then after that, I went on to the strip and continued to break every casino. (I also turned in my two snowglobes, 1 from goodsprings and one from the lucky 38 for another 4k).
So I was level 2, in new vegas with about 40k in caps and loaded to the teeth with energy weapons like the plasma caster and combat armor.

It was kinda funny, cus house told me that Ive come a long way, and haven't kept a low profile. Which is messed, cus my character literally made it to vegas in a day from getting shot in the head.
But yeah, that was the earliest I made it to the strip. I wanted to be level 1, but killing that single cazadore was unavoidable and It happened to level me up.

I have gotten there the quick back way, and it was about as tough as you described. The problem is, I arrived at the strip too early to pass any of the Speech Checks in the first act of the MQ. I have found that by following the first act, I arrive in Freeside/Strip at about level 10 with my skills where they need to be to pass the challenges. No matter what I do with the MQ, which is usually ignore it, I do the first act of the MQ up to the meeting at the Fort. I just like the changes in the game that occur after that (like not having to talk to Victor anymore)