My first SAT mock test score without any preparation was 1880, can i pull off a 2300+ score in one month?

No.

Seriously? No. I got a 2200 on my first try, and slacked off thinking I had it made. I dropped the next time expecting to get an easy 2300, which brought my cumulative score down. Jumping from a 1800 to a 2300 is not unheard of, but HIGHLY unlikely. Then again, I'm asian, and we automatically have minimum 2100's. Different standards lol.

It's easier to go up 100 points than it is to go that huge jump I certainly wouldn't expect your score to rise up that quickly at all.

One month is a little tough but it is entirely possible to experience a dramatic jump in score. I went from 1770-2230 (that is a 460 point jump) with 3 months prep beforehand. With that being said, so long as you buy the College Board Practice Test book, take the practice tests by replicating testing conditions, and check over the answers to understand what you got wrong, you should be able to see a rise in scores. How high I do not know. Anything 2300+, in my opinion, is luck-based anyways. It really depends on the curve of each section and how difficult a particular section was for the past month.

No one can really answer that but you. Did you try at all on the first test? If you didn't study, but still did your best, I'd say the chances of a 2300+ are slim. If you didn't take it seriously.. maybe. Honestly, I have a hard time seeing a 600 point jump. Students who spend way too much money on test prep courses typically get a 200 pt increase, tops. Have you taken the PSAT before? That can be a good predictor of your SAT scores. If you can, take another mock exam, or find one in a test prep guide. You may find that you have to lower your standards. A 2100 is by no means a low score, but a 300 point jump is more conceivable than a 600 pt jump. (Rob, I'm Asian, and I don't think 2100 is an automatic for all of us..)