To be a CA you have to have one of two:
A) 2,500TT 1,000 SIC
Or
B) 2,000TT 1,000SIC with 1,500 multi (might be the best option of your eligible for the ATP reduced time)
So starting off the bat you need a minimum of a 1000 hours.
Thinking about FAR 117, you can max 1,000 in a year but do you really think you'll be able to get that? So realistically you looking at a year a half to even be eligible.

Another option, If your coming in with a restricted time reduction (Getting the ATP at 1,000) then you would need 1500 hours to reach the 2500TT. Or may go with option B since its lower Total time, but then you have to think about the multi time you have. This could mean you a couple hundred more hours of multi on top of the 1000 you'll get SIC, so in this case you may need 1200-1400hrs of time in the right seat to hit all the minimums. This would probably take 18-24 months MINIMUM just to be eligible.

Something to keep in mind about upgrading with no 121 experience.