Using reconfigurable fluid antennas, it is possible to have a software‐controlled position‐tuneable antenna to realize spatial diversity and multiplexing gains that are previously only possible using multiple antennas. Recent results illustrated that fast fluid antenna multiple access (f‐FAMA) which always tunes the antenna to the position for maximum signal‐to‐interference ratio (SIR) on a symbol‐by‐symbol basis, could support hundreds of users on the same radio channel, all by a single fluid antenna at each user without complex coordination and optimization. The network outage rate, nevertheless, depends on the SIR threshold chosen for each user. Motivated by this, this paper adopts a first‐order approximation to obtain the outage probability expression from which a closed‐form solution is derived for optimizing the SIR threshold in maximizing the network outage rate. Moreover, a closed‐form expression is provided to estimate the number of users in the f‐FAMA network in which the outage rate begins to plateau. Numerical results show that the proposed SIR threshold achieves near‐maximal outage rate performance.