Partonic matter produced in the early stage of ultrarelativistic nucleus-nucleus collisions is assumed to be composed mainly of gluons, and quarks and antiquarks are produced at later times. To study the implications of such a scenario, the dynamical evolution of a chemically nonequilibrated system is described by the ideal (2+1)-dimensional hydrodynamics with a time dependent (anti)quark fugacity. The equation of state interpolates linearly between the lattice data for the pure gluonic matter and the lattice data for the chemically equilibrated quark-gluon plasma. The spectra and elliptic flows of thermal dileptons and photons are calculated for central Pb+Pb collisions at the CERN Large Hadron Collider energy of $\sqrt{s_{_{\rm NN}}} = 2.76$ TeV. We test the sensitivity of the results to the choice of equilibration times, including also the case where the complete chemical equilibrium of partons is reached already at the initial stage. It is shown that a suppression of quarks at early times leads to a significant reduction of the yield of the thermal dileptons, but only to a rather modest suppression of the $p_T$-distribution of direct photons. It is demonstrated that an enhancement of photon and dilepton elliptic flows might serve as a promising signature of the pure-glue initial state.