The Mamyshev oscillator (MO) is a promising platform to generate high-peak-power pulse with environmentally stable operation. However, rare efforts have been dedicated to unveil the dynamics from seed signal to oscillator pulse, particularly for the multi-pulse operation. Herein, we investigate the buildup dynamics of the oscillator pulse from the seed signal in a fiber MO. It is revealed that the gain competition among the successively injected seed pulses leads to higher pump power that is required to ignite the MO, hence resulting in the higher optical gain that supports buildup of multiple oscillator pulses. The multiple oscillator pulses are identified to be evolved from the multiple seed pulses. Moreover, the dispersive Fourier transform (DFT) technique is used to reveals the real-time spectral dynamics during the starting process. As a proof-of-concept demonstration, a highly intensity-modulated pulse bunch was employed as the seed signal to reduce the gain competition effect and avoid the multi-pulse starting operation. The experimental results are verified by numerical simulations. These findings would give new insights into the pulse dynamics in MO, which will be meaningful to the communities interested in ultrafast laser technologies and nonlinear optics.