The nature of the first galaxies that reionised the universe during the Epoch of Reionisation (EoR) remains unclear. Attempts to directly determine spectral properties of these early galaxies are affected by both limited photometric constraints across the spectrum and by the opacity of the intergalactic medium to the Lyman Continuum (LyC) at high redshift. We approach this by analysing properties of analogous extreme emission line galaxies (EELGs, [OIII]+Hbeta EW
$\gt 400$) at
$2.5\lt z\lt 4$ from the ZFOURGE survey using the Multi-wavelength Analysis of Galaxy Physical Properties (MAGPHYS) SED fitting code. We compare these to galaxies at
$z \gt 5.5$ observed with the James Webb Space Telesope with self-consistent spectral energy distribution fitting methodology. This work focuses on the comparison of their UV slopes (
${\unicode{x03B2}}_P$), ionising photon production efficiencies
$\xi_{ion}$, star formation rates and dust properties to determine the effectiveness of this analogue selection technique. We report the median ionising photon production efficiencies as log
$_{10}(\xi_{ion}/(Hz\ {\rm erg}^{-1}))=$
$25.14^{+0.06}_{-0.04}$,
$25.16^{+0.06}_{-0.05}$,
$25.16^{+0.04}_{-0.05}$,
$25.18^{+0.06}_{-0.07}$ for our ZFOURGE control, ZFOURGE EELG, JADES, and CEERS samples, respectively. ZFOURGE EELGs are 0.57 dex lower in stellar mass and have half the dust extinction, compared to their ZFOURGE control counterparts. They also have a similar specific star formation rates and
${\unicode{x03B2}}_P$ to the
$z\gt 5.5$ samples. We find that EELGs at low redshift (
$2.5\lt z\lt 4$) are analogous to EoR galaxies in their dust attenuation and specific star formation rates. Their extensive photometric coverage and the accessibility of their LyC region opens pathways to infer stellar population properties in the EoR.