The increasing interest of fluid antenna systems is reinforced by an unprecedented way of achieving multiple access, by exploiting moments of deep fades in space. This phenomenon, referred to as fluid antenna multiple access (FAMA), allows the fluid antenna at each user to be switched to a location in space (i.e., port) where the sum-interference power collectively suffers from a deep fade, resulting in a decent signal reception without the need of complex signal processing. Nevertheless, selecting the best port is an arduous task, which requires a large number of channel observations to obtain the high performance gain. This letter aims to devise a low-complexity port selection scheme for FAMA where each user has a small number of port observations only. We assume slow FAMA (s-FAMA) so that the selected port remains unchanged until the channel conditions change. A deep learning approach is proposed to infer the signal-to-interference plus noise ratios (SINR) at all the available ports given only a small number of observations. The simulation results exhibit that the proposed scheme is able to attain significant reductions in outage probability, and improvements in multiplexing gain, from a relatively small number of available port observations, showing great potential for future multiple access technologies.