Prior to answer this question I would like to see your appointment letter or offer letter
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It is very smart of you not to sign the agreement before consulting a professional as sometimes employers may exploit unaware employees. I recommend you share the agreement with a professional for review who can pinpoint the things which go against your interest and thereafter negotiate the same with the employer. For now, ask them to amend the agreement and change your date of joining to a date after 4th of october. You can be honest with your employer that you don't feel comfortable signing an agreement before changes as an agreement once signed can not be changed, only amended.
In case you want the entire offer letter be reviewed please contact: firstname.lastname@example.org