One idea I had for an "Immersive" Mojave start could go something like this:
Okay the fallout 3 video plays, Baby scene from the Cap Wasteland starts. You are born, your dad gives you your name, gene projection, mom dies, etc.
Right at this moment, you are given the option: "Is this a dream? Or is this reality? Do you wake up, or do you continue living the dream a while longer?"
If you choose to "wake up", a messagebox pops up that says "as you struggle to get yourself out of the dream, your life flashes before your eyes. In mere moments, 20 whole years flash before your eyes."
This cues another intro movie (NOT the FONV one) which is a very abridged version of your life in vault 101 and the cap wasteland. Starts with a with you as a baby going up to the "IM SPECIAL" book. Skip to dad saying "Revelation 21:6", Which skips to your birthday starting, which skips to butch saying "Gimmie that sweetroll", Then flashing forward to dad giving you the bb gun, then to you killing the radroach, then to dad saying "Goat Exam" Then to butch teasing amata, then to Brotch saying "You passed the goat", Then to Amata waking you up and saying "You've got to get out of here", Then to you shooting officer Mack, then to you opening the vault door, then to you looking around outside.
Then it flashes forward to inside megaton where Lucas says "I'm Lucas Simms" Followed by "No, haven't seen anyone like that" Followed by you shooting up some raiders, then to you throwing a nade at some super mutants, followed by you finding the train station, then by you entering the train station.
It's a lot shorter than it sounds. Basically a super-abridged version of your time in the cap wasteland.
After this is done, you get a messagebox that says "As your distant past fades away, your more recent history catches up to you...." Cue the new Vegas intro, followed by the Doc Mitchel scene.
However, if you choose to remain asleep a while longer, the normal vault 101 scenes continue, up untill the escape from vault 101 part. Here you are given one more chance to start in the mojave again just as you open the vault door and step outside into the cave. A messagebox appears, along with a ghostly sounding voice of Doc Mitchell. The messagebox says "You hear a voice in your head, telling you to awaken. Question is, are they reality, or a figment of your imagination. Do you give into the kind, elderly voice, or pass it off as your imagination?"
If you pass it off, nothing happens. You reach the vault cave door, capital wasteland start.
However, if you choose to give into the voice, you instead get another flash of light, followed by another messagebox. This one says "As your dream of your life long past fades around you, a flashback of your more recent history rushes into your mind."
Then, "9 Years Later", followed by the New Vegas intro, and you wake up in Doc Mitchell's office. Que normal TTW FONV Doc Michell scene.
There you go. Two chances to start in New Vegas. Both a really fast way, and a slow but more immersive way.