Deep learning approaches have emerged that aim to transform an audio signal so that it sounds as if it was recorded in the same room as a reference recording, with applications both in audio post-production and augmented reality. In this work, we propose FiNS, a Filtered Noise Shaping network that directly estimates the time domain room impulse response (RIR) from reverberant speech. Our domain-inspired architecture features a time domain encoder and a filtered noise shaping decoder that models the RIR as a summation of decaying filtered noise signals, along with direct sound and early reflection components. Previous methods for acoustic matching utilize either large models to transform audio to match the target room or predict parameters for algorithmic reverberators. Instead, blind estimation of the RIR enables efficient and realistic transformation with a single convolution. An evaluation demonstrates our model not only synthesizes RIRs that match parameters of the target room, such as the $T_{60}$ and DRR, but also more accurately reproduces perceptual characteristics of the target room, as shown in a listening test when compared to deep learning baselines.