Like getting an appointment letter from the Government, leaving a Central Government job may also take time. It is also complicated because of various procedural aspects. So, you have two alternatives in your preent circumstances.
1st alternative: You seek extension of time to join the first job. At the first instance, you can get 3 months time to join. Overall you can get 1 year to join the job. During this period , you can complete the physical test etc in respect of the second job and join the second job. After joining, decline the offer of appointment to the first office (first job).
2nd alternative: You join the first job. But immediately after joining, give intimation to the office in writing about your second job, so that later when the offer of appointment (in repect of the second job) is received, you can be relieved/you can resign as early as possible.
Come on, have a fight. Don't shoot and scoot.