Equivalence of Maximum Likelihood (ML) and Discrete Fourier Transfrom (DFT) Peak Finding for Single Tone Estimation
Maximum Likelihood under the assumption of Additive White Gaussian Noise (AWGN) is always equivalent to finding the hypothesis with the minimum distance to given data.

Since minimizing distance is equivalent (In the euclidean Space) of maximizing the correlation you can always build the idea of Match Filter for parameter estimation in the settings of ML under AWGN.

Matched filter means that you create a set of hypothesis parameterized on a grid and goes one by one until you find the one which maximizes correlation (Minimizes distance) to data.

This is exactly what's the DFT is doing.
The grid is based on the different tones (Frequencies) and the correlation level is given by the bin value.