The short duration employment from one organisation to another cannot be a hindrance to join the other organisation.
This short tenure will not be even counted for your experience then why do you rely on this.
Have you informed the new employer about the previous employment?
If not, then you dont require even NOC for this.
However you may communicate your decision to the previous employer by sending a letter by registered post and keep the acknowledgment, if you dont get any response for this, you may show this letter to the new employer and convince the ne3w employer about your inability to provide the relieving letter despite making best efforts to this.
You can even issue a legal notice through an advocate on this to the previous employer.