  Multipartite entanglement, such as witnessed through the quantum Fisher
information (QFI), is a crucial resource for quantum technologies, but its
experimental certification is highly challenging. Here, we propose an
experimentally friendly protocol to measure the QFI. It relies on recording the
short-time dynamics of simple observables after a quench from a thermal state,
works for spins, bosons, and fermions, and can be implemented in standard
cold-atom experiments and other platforms with temporal control over the system
Hamiltonian. To showcase the protocol, we simulate it for the one-dimensional
Fermi--Hubbard model. Further, we establish a family of bounds connecting the
QFI to multipartite mode entanglement for fermionic systems, which enable the
detection of multipartite entanglement at sizable temperatures. Our work paves
a way to experimentally accessing entanglement for quantum enhanced metrology.
