downgrade mavericks to 10.8 w/o clean install

No

Only way to downgrade is to erase and install

For the time being, if you had already purchased OS X 10.8 Mountain Lion in the past, you should be able to go into your purchases section on the Mac App Store and redownload and install this on a fast, external USB 3.0, Thunderbolt or FIreWire hard drive depending on what year and model iMac you have.

You can either install and run OS X 10.8 from this external hard drive.

OR get the external hard drive, use a data cloning app, like CarbonCopyCloner or SuperDuper to create a bootable clone of your entire current system to the external drive, then boot from that, use OS X Disk Utility to wipe and reformat your iMac's internal hard drive and while booted from the external drive, redownload and install OS X 10.8 Mountain Lion and install it to your iMac's internal drive.

You should be able to boot back to the internal hard drive and use the applications, that were copied to the external drive, and for the time being USs and launch them from that location until you have time to either manually transfer or manually reinstall them to your iMac's internal drive.

This is your only other option.

Hello, I am going to chime in as well.

Technically, you can downgrade if you have the following:

• Your computer must be elligible to run Mountain Lion. If your computer came with Mavericks or Yosemite out of the box, you can forget it.
• You need an already existing Mountain Lion installer file. If you still have that somewhere, for example in your Applications folder, or anywhere else, it's usable- note that it needs to be originally downloaded with your own Apple ID and password. If you made a Mountain Lion USB installer or DVD back then that would work too. If your Time Machine back-ups go back to the days of Mountain Lion or Lion you could check your Applications folder from inside Time Machine and restore it to your computer.
• To not have data loss you need a Time Machine back-up that goes back to when you were still running Mountain Lion. Please note that this will revert your data to exactly the date that you choose. If you installed Mavericks 2 months ago, you will loose 2 months worth of data.

I wasn't t going to call you out on some things, but CellarDwellr has made some interesting points.

Also, I was bothered by your, seemingly, desperate tone of your inquiry.

If you are a professional or semi-professional.

Why would you even think about upgrading to a new operating system in the middle of an important project and knowing that the client is going to show up within hours to work with you on critical project?

Why would you upgrade your system in a middle of a critical project without researching, ahead of time, whether the applications you normally use are compatible with that new system upgrade or not?

Why do you NOT have proper, multiple backup drives of your previous system configurations and all of your important data?

As a professional/semi-professional (or even as a normal computer user, for that matter) you need to have and maintain multiple backups to have some way to revert your computer system to a previous and fairly current working state in the event something goes wrong with your computer hardware or system, computer upgrade/update issues or you experience hard drives that can and do fail over time.

You ou need to be using both Time Machine AND data cloning apps to create multiple and bootable external hard drive backups.

Hello again.

Since your computer came out of the box with Mavericks, I'm afraid any hopes of downgrading are in vain. It won't work. You'll have to find a computer with Mountain Lion, postpone the deadline or maybe figure out something else.

the computer is new and shipped with Mavericks

Than you can't go "backwards" with or without an erase - Macs cannot boot from an OS version older than what they came with. Unless this machine has a build from right around the time that Mavericks was introduced, it may be able to boot with ML, otherwise not.

The app Mactracker would be a good way to figure out what the original OS was your model shipped with:

https://itunes.apple.com/nl/app/mactracker/id430255202?mt=12

Right here:

Mac OS X versions (builds) for computers - Apple Support

iMac 14,2 is only compatible with Mountain Lion.

Yours is a late 2013 - looking at Apple's info, early iterations came with ML and later builds with mavericks. I'd suggest contacting Apple and asking which build yours came with originally; they should be able to tell with your serial number.