If we are using the LSE "least square error" equation for getting the AR and MA terms: by getting the LSE in function of the coefficients and differencing it then equating it to zero.This yields to getting the coefficients using only one step "one iteration" My question is where does the iterations comes from for fitting an ARIMA model??
When you can analytically solve for a minimum in the negative log-likelihood (or your loss function), then there is indeed only the step of solving an equation.
When you instead use some algorithm to iteratively find your minimum, you start at some initial point, have some rule on how to update for the next iteration and keep updating the parameter values. You iterate until some convergence criteria are met that indicate whether a minimum has been reached.