Honestly I want a game where they start off scum (details below for those who care) and slowly work their way up. The thing is it would take a very long time to do that properly so this is a sort of compromise a few runs for their backstory as they work their way up and everyone can get a handle on the rules then the regular game from normal levels.
Basic idea is a bunch of scum no job, no future, no sin, no hope receive a message "Are you tired of your life, want something new? Something better? Something you could never hope to achieve in the world as it stands no matter how hard you try? Then come to XXXXXX at XX:XX.". Most of them ignore it but a few (the pc's) are still hopeful enough, or desperate and go to the meeting in a large office tower that's empty of anyone else. A bunraku takes them up to the 55th floor and sets up a computer. On the other side is a Japanese man who tells them that Japan is currently a place of opportunity and advantage and this is their lucky day because the company he works for has a unique offer to make, contracts are uploaded to their comlinks. They will be given contacts, travel and opportunity to prove themselves (raise enough money to purchase the medium lifestyle or higher permanently, 500k nuyen). Should they succeed they will receive a corporate SIN, office and work directly for the company. Fail (as defined by being prominently identified, failing to raise the money, generating enough problems that later identification will embarass the company etc etc . . . probably a hand waved 12-16 lines of failure clauses) and they'll still retain all they've earnt they just wont receive the corporate SIN and office work (which is still the same work just jobs where they have less need of deniability e.g. surveiling a prominent official, protecting corporate facilities, legtimate jobs such as investigating an artifiact found by the company.). Once they accept and sign it they receive a fake sin (rating 3), passport and ticket to Japan (flight non-negotiable as if they miss it the security forces will almost certainly arrest them for using a fake sin, they weren't bribed in other words), a booking resrvation for 1 week at a coffin hotel and a name, address and time to meet a fixer who will handle their jobs. Obviously failure to comply with any of these requirements counts as forfeiture on the contract.
Like I said if I thought I could raise them up to normal levels fast enough I'd not be time skipping at all. I might do more runs at each level depending on how it goes too.