In this first paper of the series , we present initial results of newly upgraded Giant Meterwave Radio Telescope ( uGMRT ) observation of European Large-Area ISO Survey-North 1 ( ELAIS-N1 ) at 325 MHz with 32 MHz bandwidth . Precise measurement of fluctuations in Galactic and extragalactic foreground emission as a function of frequency as well as angular scale is necessary for detecting redshifted 21-cm signal of neutral hydrogen from Cosmic Dawn , Epoch of Reionization ( EoR ) and post-reionization epoch . Here , for the first time we have statistically quantified the Galactic and extragalactic foreground sources in the ELAIS-N1 field in the form of angular power spectrum using the newly developed Tapered Gridded Estimator ( TGE ) . We have calibrated the data with and without direction-dependent calibration techniques . We have demonstrated the effectiveness of TGE against the direction dependent effects by using higher tapering of field of view ( FoV ) . We have found that diffuse Galactic synchrotron emission ( DGSE ) dominates the sky , after point source subtraction , across the angular multipole range 1115 \leqslant \mathcal { \ell } \leqslant 5083 and 1565 \leqslant \mathcal { \ell } \leqslant 4754 for direction-dependent and -independent calibrated visibilities respectively . The statistical fluctuations in DGSE has been quantified as a power law of the form \mathcal { C } _ { \mathcal { \ell } } = A \mathcal { \ell } ^ { - \beta } . The best fitted values of ( A , \beta ) are ( 62 \pm 6 mK ^ { 2 } , 2.55 \pm 0.3 ) and ( 48 \pm 4 mK ^ { 2 } , 2.28 \pm 0.4 ) for the two different calibration approaches . For both the cases , the power law index is consistent with the previous measurements of DGSE in other parts of sky .