Time reversal (TR) is a promising technique that exploits multipaths for achieving energy focusing in high-frequency wideband communications. In this letter, we focus on a TR scheme facilitated by a reconfigurable intelligent surface (RIS) which, due to the higher frequency and large array aperture, operates in the near-field region. The proposed scheme enriches the propagation environment for the TR in such weak scattering conditions and does not need channel knowledge for the RIS configuration. Specifically, the RIS is employed to create multiple virtual propagation paths that are required to efficiently apply the TR. We derive a performance bound for the proposed scheme under near-field modeling through the received signal-to-noise ratio (SNR) and we examine how various system design parameters affect the performance. We observe that a linear RIS topology maximizes the number of resolvable paths. It is also demonstrated that the proposed scheme improves the SNR, while for a large number of elements it can outperform the conventional passive beamforming at the RIS.