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With the advent of billion-galaxy surveys with complex data, the need of the hour is to efficiently model galaxy spectral energy distributions (SEDs) with robust uncertainty quantification. The combination of Simulation-Based inference (SBI) and amortized Neural Posterior Estimation (NPE) has been successfully used to analyse simulated and real galaxy photometry both precisely and efficiently. In this work, we utilise this combination and build on existing literature to analyse simulated noisy galaxy spectra. Here, we demonstrate a proof-of-concept study of spectra that is a) an efficient analysis of galaxy SEDs and inference of galaxy parameters with physically interpretable uncertainties; and b) amortized calculations of posterior distributions of said galaxy parameters at the modest cost of a few galaxy fits with MCMC methods. We utilise the SED generator and inference framework Prospector to generate simulated spectra, and train a dataset of 2$\times$10$^6$ spectra (corresponding to a 5-parameter SED model) with NPE. We show that SBI -- with its combination of fast and amortized posterior estimations -- is capable of inferring accurate galaxy stellar masses and metallicities. Our uncertainty constraints are comparable to or moderately weaker than traditional inverse-modeling with Bayesian MCMC methods (e.g., 0.17 and 0.26 dex in stellar mass and metallicity for a given galaxy, respectively). We also find that our inference framework conducts rapid SED inference (0.9-1.2$\times$10$^5$ galaxy spectra via SBI/SNPE at the cost of 1 MCMC-based fit). With this work, we set the stage for further work that focuses of SED fitting of galaxy spectra with SBI, in the era of JWST galaxy survey programs and the wide-field Roman Space Telescope spectroscopic surveys.