Switching Job

I have received an offer letter from X company with a mid-June joining date. Since there were few or no dependencies on me at my current company, Y, I have resigned and will be available in a month, with today being my last day. I have attempted to contact my new recruiter via calls and messages to discuss preponing my joining date, but she has not been responding actively. Today marks the third day of attempting to reach her. I plan to call her again this afternoon, as I understand she may be busy. However, I would prefer to discuss this matter over a call to expedite my joining process. Should I attempt to call her again, considering she mentioned being busy yesterday? How can I approach her politely, without sounding desperate? Alternatively, do you have any other suggestions?