Want to leave company without notice period and experience letter in probation period

AkkiMumbai
I join one company 1 month back and found that job profile is not as per discussed in interview so I started looking for new company. I got one offer from one company that "Join us immediately without serving notice period and we will mention your joining data as one month back". shall I accept this offer ? this offer looking good to me. If I leave current company without serving notice period then what action can be taken against me ?
In my appointment letter, it is clearly mention that in probation period I have to serve 1 month notice period or pay full salary in lie. Also company is liable to take induction & training cost from the employee.
Please suggest.
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