Systems for synthesizer sound matching, which automatically set the parameters of a synthesizer to emulate an input sound, have the potential to make the process of synthesizer programming faster and easier for novice and experienced musicians alike, whilst also affording new means of interaction with synthesizers. Considering the enormous variety of synthesizers in the marketplace, and the complexity of many of them, general-purpose sound matching systems that function with minimal knowledge or prior assumptions about the underlying synthesis architecture are particularly desirable. With this in mind, we introduce a synthesizer sound matching model based on the Audio Spectrogram Transformer. We demonstrate the viability of this model by training on a large synthetic dataset of randomly generated samples from the popular Massive synthesizer. We show that this model can reconstruct parameters of samples generated from a set of 16 parameters, highlighting its improved fidelity relative to multi-layer perceptron and convolutional neural network baselines. We also provide audio examples demonstrating the out-of-domain model performance in emulating vocal imitations, and sounds from other synthesizers and musical instruments.