1st day CPT for first master and getting H1 after that

I am legally staying in US on H4 visa. My educational background is bachelor in Engineering. I dont have EAD and also my H1 did not pick in lottery. So I am thinking about other options.

  1. I am thinking about converting to F1 and start course in university with 1st day CPT. Are these courses legal?
    2.Will there be any problem if I try to convert to H1b next year?
  2. If you know any other options let me know.
  1. Day 1 CPT universities are really subject to lot of Fraud and there were many situations where they ran into trouble…while there are some who are successful, but Day 1 CPT schools are risky…
  2. Well, instead you find a job at a cap exempt location like University or Non-profit research institute.