  We propose a new method for obtaining an effective
Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmology from the quantum gravity
dynamics of group field theory (GFT), based on the idea that an FLRW universe
is characterised by a few macroscopic observables. Rather than relying on
assuming a particular type of quantum state and computing expectation values in
such a state, here we directly start from relations between macroscopic
observables (defined as one-body operators) and formulate dynamics only for
those observables. We apply the effective approach to constrained quantum
systems (as developed by Bojowald and collaborators) to GFT, providing a
systematic expansion in powers of $\hbar$. We obtain a kinematical phase space
of expectation values and moments, which does not require an a priori choice of
clock variable. We identify a gauge fixing of the system which corresponds to
choosing one of the cosmological variables (with the role of extrinsic
curvature) as a clock and which allows us to rewrite the effective dynamics in
relational form. We show necessary and sufficient conditions for the resulting
dynamics of expectation values to be compatible with those of classical FLRW
cosmology and discuss the impact of quantum fluctuations.
