This paper studies a wireless-energy-transfer (WET) enabled massive multiple-input-multiple-output (MIMO) system (MM) consisting of a hybrid data-and-energy access point (H-AP) and multiple single-antenna users. In the WET-MM system, the H-AP is equipped with a large number $M$ of antennas and functions like a conventional AP in receiving data from users, but additionally supplies wireless power to the users. We consider frame-based transmissions. Each frame is divided into three phases: the uplink channel estimation (CE) phase, the downlink WET phase, as well as the uplink wireless information transmission (WIT) phase. Firstly, users use a fraction of the previously harvested energy to send pilots, while the H-AP estimates the uplink channels and obtains the downlink channels by exploiting channel reciprocity. Next, the H-AP utilizes the channel estimates just obtained to transfer wireless energy to all users in the downlink via energy beamforming. Finally, the users use a portion of the harvested energy to send data to the H-AP simultaneously in the uplink (reserving some harvested energy for sending pilots in the next frame). To optimize the throughput and ensure rate fairness, we consider the problem of maximizing the minimum rate among all users. In the large-$M$ regime, we obtain the asymptotically optimal solutions and some interesting insights for the optimal design of WET-MM system. We define a metric, namely, the massive MIMO degree-of-rate-gain (MM-DoRG), as the asymptotic UL rate normalized by $\log(M)$. We show that the proposed WET-MM system is optimal in terms of MM-DoRG, i.e., it achieves the same MM-DoRG as the case with ideal CE.